How a manhunt works, according to security experts.

Officials have pleaded for help from the public, offering a $50,000 reward for information leading to Mr. Boelter’s arrest. At the same time, they urged caution, saying he was believed to be armed, dangerous and willing to kill. State investigators scheduled a news conference to provide updates on the case at 5:30 p.m. Central time.

Communities were on edge around the Minneapolis suburbs where the authorities say the suspect went to the homes of two lawmakers early Saturday, pretending to be a police officer. According to investigators, he was wearing a ballistic vest, gloves and an identity-disguising mask as he killed Representative Melissa Hortman and her husband, Mark. The police almost caught the suspect at the home, but he escaped on foot after exchanging gunfire with officers.

State Senator John A. Hoffman, a fellow Democrat, and his wife, Yvette, were also shot in a separate attack but survived. Senator Amy Klobuchar of Minnesota said on NBC’s “Meet the Press” on Sunday that the couple were “hanging in there.” Mr. Hoffman, she said, “may face some additional surgeries, but he is also in stable condition right now, from what I know.”

Investigators have been examining surveillance footage, bank records, Mr. Boelter’s associations and his movements from before the shootings. He had been politically engaged: A friend said he opposed abortion and had supported President Trump, and he previously served on a state work force development board with Senator Hoffman.

Here’s what else we know:

• The victims: Ms. Hortman served as speaker of the Minnesota House for a six-year period that ended this year and helped pass several key policies on abortion rights, marijuana legalization and medical leave. Mr. Hoffman is a fourth-term state senator from Champlin, another Minneapolis suburb, and leads the Senate’s Human Services Committee. Read more ›

• The suspect: Mr. Boelter and his wife run a private security company that promotes the usage of S.U.V.s similar to those used by police departments, according to its website. The couple also appears to have run a religious nonprofit. An archived version of the organization’s website described Mr. Boelter as an ordained minister who had preached overseas. It said that he “sought out militant Islamists in order to share the Gospel and tell them that violence wasn’t the answer.” Read more ›

• Political violence: Slowly but surely, violence has moved from the fringes to become part of the political landscape. Threats and even assassinations, attempted or successful, have become a steady undercurrent of American life. Read more ›

But in the hours after the shootings, while police officers were still searching for the assassin, lawmakers across the country began to rethink their approach to privacy and safety. The Michigan State Police held security briefings for legislators. The police in Fairfax County, Va., increased patrols around lawmakers’ homes. And in North Dakota, officials decided by midday Saturday to scrub home addresses from legislator biography pages.

“In light of the tragedy in Minnesota, we quickly decided to remove all addresses until our leaders have time to assess the proper balance between transparency and safety of our elected officials,” John D. Bjornson, the director of the North Dakota Legislative Council, said in an email.

In interviews with lawmakers across the country, some said sharing their home address helped reassure constituents that they were part of the community and could be easily reached. But unlike governors and presidents, most state lawmakers have no special security protection when they are away from work. The country’s coarsening public discourse has left them to weigh difficult trade-offs.

“Part of the reason why my address is easily found is to make it clear that I actually live in my district,” said Stephanie Sawyer Clayton, a Democratic state representative in Kansas. “If you have a P.O. box, you don’t look authentic, right?”

“But for authenticity,” Ms. Clayton added, “you kind of pay that price of vulnerability.”

Though recent political violence has cut across party lines, both Minnesota lawmakers who were shot were Democrats, and the suspected assassin was said to be carrying a list of targets that was filled with more Democrats.

In Ohio, State Senator Casey Weinstein thanked his state’s Republican governor on Saturday for increasing security for lawmakers, a decision that the governor’s office declined to confirm.

“Honestly I’m struggling with this news,” Mr. Weinstein, a Democrat, wrote on Facebook after the Minnesota attacks. “I’m worried for my family. I worry I’m putting them in harm’s way by being in office. It’s a terrible feeling.”

In Michigan, State Representative Karen Whitsett said she had no plans to remove her home address from her campaign website.

But Ms. Whitsett, a Democrat who sometimes votes with Republicans in her state’s closely divided Legislature, said she had faced threats over the years.

After the Minnesota attack, Ms. Whitsett said she decided to seek a permit to carry a concealed gun. Ms. Whitsett said she previously had such a permit and used it to carry a weapon inside the State Capitol, where she does not always feel safe. She plans to do so again.

“I’m not going to depend on security,” said Ms. Whitsett, who on Sunday attended a video briefing on legislator safety that the Michigan State Police scheduled after the Minnesota attacks.

Another Michigan state representative, Bill G. Schuette, a Republican, said he had purchased a home security system in recent years after angry people showed up at his house on multiple occasions. His address, he said, was required to be public under state law.

“You sign up in this business to be accessible to your constituents and to be a voice that’s always listening,” Mr. Schuette said. “You really have to be grateful and thankful for our brave women and men in law enforcement, and hopeful, too, that people will try and respect some personal boundaries.”

In North Dakota, State Senator Ryan Braunberger said he had been comfortable with his address being posted online before state officials decided to take it down this weekend. Mr. Braunberger, the Democratic leader in his chamber, said he had heard from the police in his home city of Fargo that they would be increasing patrols near legislators’ homes following the shootings near Minneapolis, about three hours away by car.

“Honestly I don’t feel unsafe today,” he said. “But I also refuse to live in that world of fear, because it only encourages the perpetrators. Because that’s what they’re trying to do, is incite fear.”

Todd McGhee, a law enforcement and security analyst and former Massachusetts state trooper, said that officials typically use several avenues to track down suspects, including debit and credit card payments, social media posts and location data from cellphone towers.

Rob D’Amico, a retired F.B.I. agent and security expert, said the authorities would be looking for any vehicles the suspect could be driving, burner phones he could be using, accomplices he might have had and any information found on computers or devices left at his home.

Investigators are often hoping suspects will make errors that help reveal their locations. People on the run “are usually not thinking clearly,” Mr. McGhee said.

“They’ve had very strategic plans on their attack,” he added. “They’ll know the movements of their target. They’ll understand the best time of day and location as to where to attack. But after the attack, those strategic plans begin to erode.”

Mr. D’Amico said if the gunman had not previously planned his escape, a lack of sleep and pressure to avoid authorities could affect his decision-making.

“He could do dumb things, and sometimes they get caught when they do dumb things,” Mr. D’Amico said. “Or they could do desperate things, which can lead to more violent encounters.”

The fact that the gunman shot not only the lawmakers but their spouses could suggest that he is willing to harm anyone caught in the crossfire of his political targets, Mr. D’Amico said.

As of Sunday afternoon, there was a significant police presence near the rural area in Sibley County where the car believed to belong to Mr. Boelter was found. In rural areas, a suspect may remain hidden for longer, with fewer people around to contribute to the search, Mr. D’Amico said, but the lower population density makes it easier to use certain technologies, such as thermal imaging helicopters.

Though several high-profile manhunts in recent years may come to mind, including after the killing last year of the chief executive of UnitedHealthcare in Manhattan and after the 2023 shootings in Lewiston, Maine, in which 18 people died, Mr. D’Amico cautioned that each suspect thinks differently.

“You can’t compare,” he said.

Jonathan Wolfe contributed reporting.

The Sibley County administrator, John Gliczinski, said he was aware that an emergency alert had been issued in the area. He said he was not personally involved in issuing it and did not have further information.

“What happened today is simply incomprehensible and unimaginable, certainly in the context of Minnesota,” Norm Coleman, a former senator from Minnesota and former mayor of St. Paul, said in an interview on Saturday. He ticked off a list of Republican and Democratic politicians who had reached across the aisle — Hubert Humphrey, Tim Pawlenty and Amy Klobuchar. “It’s a history of people who tried to find common ground.”

Authorities in Minnesota were still trying to capture the 57-year-old man who has been identified as the suspect in the shootings that took place early Saturday in the quiet suburbs of the Twin Cities. But they said that it was a “politically motivated” act of violence, and that the suspect had papers in his car that indicated he may have been planning to target one of the “No Kings” protests taking place in the state or cities across the country on Saturday.

Even as the national political discourse has grown hyperpartisan in recent years, Minnesota has kept a foothold on its own traditions, formed by a long line of politicians who were known for their openness and bipartisanship approach. Some lawmakers, including State Senator John A. Hoffman, a Democrat who was shot in the attacks overnight, still posted their home addresses online. State Representative Melissa Hortman, a Democrat, was killed in the attacks, along with her husband, Mark, and Mr. Hoffman and his wife, Yvette, were seriously wounded.

Minnesota, one of only three states with a legislature where control is split between Democrats and Republicans, consistently has higher voter turnout than any other state, with 76 percent of voting-age citizens casting ballots in the 2024 presidential election.

“It’s a state where people are highly engaged,” said Alex Conant, a Republican political strategist who has worked on campaigns in Minnesota. “It has one of the best political press corps in the country because there’s a lot of interest in politics. It’s one of the last states to have a robust caucus system, which requires high levels of grass-roots engagement from both parties. Instead of having primaries, where it’s TV ads and turnout operations, it’s caucus systems where neighbors talk to each other about who the nominee is going to be.”

Senator Tina Smith of Minnesota said on Saturday that she was “shattered” by the news of the shootings, having just seen Ms. Hortman on Friday evening at an annual Democratic Party dinner. Ms. Hortman was respected by lawmakers on both sides of the aisle, she said, someone who “had this way of being real with people.”

“It’s that attitude of, ‘I’m not going to spin you, don’t try to spin me,’” she said. “Let’s just talk for real about what we’re trying to get done here.”

Senator Smith said she believed the shootings marked “a very dangerous moment in our country.”

“I think Minnesota is very proud of our civic culture and our belief in the strength of the civic institutions,” she said. “While we certainly have our fights in the Legislature — and I was privy to many of those fights — it never rose to the level of the kind of animosity that we have seen in other parts of the country and Washington, D.C. To see this terrible violence and hatred infecting the political realm in Minnesota is just terrifying to behold.”

Among longtime political observers in Minnesota, there is a deepening sense that the state is changing along with the rest of the country.

While Gov. Tim Walz of Minnesota, a Democrat, began his political career representing a rural, conservative Congressional district, that career arc seems less imaginable today. The urban-rural divide in Minnesota has become more intense, political strategists said, and the nationalization of party politics has weighed more heavily on voters than local issues.

“I don’t see Minnesota as unique anymore,” said Ryan Dawkins, an assistant professor of political science at Carleton College in Northfield, Minn., who studies American politics and polarization. “A lot of the unique character of state politics is not gone by any stretch, but it has become much more muted as polarization has increased.”

Former Gov. Tim Pawlenty of Minnesota, a Republican who was elected in 2002 and re-elected in 2006, pointed to the state’s “nation-leading levels of civic engagement and political civility.”

But he acknowledged that it is no longer the Minnesota it used to be. “While we still cling to it,” he said, “even here it’s slipping away.”

Mr. Boelter and Senator Hoffman attended a virtual meeting together in 2022 for a discussion about the job market in the aftermath of the coronavirus pandemic, minutes from the meeting show.

Drew Evans, the superintendent of the Minnesota Bureau of Criminal Apprehension, said investigators did not yet know how well the two knew each other, if at all.

Mr. Boelter was appointed to the board in 2016 by Mark Dayton, a Democrat who was then the governor. More recently, he was appointed by Gov. Tim Walz, also a Democrat. The board has 41 members who are appointed by the governor, and its goal is to improve business development in the state.

A state report in 2016 listed Mr. Boelter’s political affiliation as “none or other,” and another report in 2020 listed him as having “no party preference.” Voters do not declare political affiliation when they register in Minnesota.

The police have said that the suspect in the attacks disguised himself as a police officer and went to the homes of two state lawmakers in the Minneapolis suburbs. He shot and wounded Senator Hoffman, and his wife, Yvette, and fatally shot State Representative Melissa Hortman, and her husband, Mark. He remains on the run.

U.S. Senator Tina Smith, Democrat of Minnesota, said in an interview that the gunman had a list that included her name and the names of other lawmakers, all of whom were Democrats. The list included about 70 potential targets, a federal law enforcement official said, including doctors, community and business leaders, and locations for Planned Parenthood and other health care centers. Some of the targets were in neighboring states.

David Carlson lives at an address in Minneapolis where the police executed a search warrant for Mr. Boelter and said he has been one of his best friends since fourth grade. Mr. Boelter’s listed address is in Green Isle, Minn., about an hour’s drive away. Mr. Carlson said that Mr. Boelter also rented a room in the same home as him, and stayed there several days a week.

Mr. Boelter worked at a funeral home, owned guns and had voted for President Trump last year, he said.

Mr. Carlson read a text message that he had received from Mr. Boelter early on Saturday morning, in which he wrote that he might be dead soon. The message did not describe any details of the attacks, Mr. Carlson said.

On Friday, Mr. Boelter had given Mr. Carlson four months’ worth of advance rent payments — which was about $220 a month — for a small room in the shared house. He had said he needed some rest and so Mr. Carlson left him alone.

Mr. Carlson said Mr. Boelter is a Christian who strongly opposed abortion. He had never mentioned either of the lawmakers who were shot, Mr. Carlson said, and had generally avoided talking about politics. He said Mr. Boelter had been experiencing financial and mental health challenges.

Mr. Boelter and his wife run a private security company in Minnesota, according to its website. The company, Praetorian Guard Security Services, lists Mr. Boelter as the director of security patrols and his wife as the president. The firm’s website describes using Ford Explorer S.U.V.s, “the same make and model of vehicles that many police departments use.”

On Saturday afternoon, the police towed a Ford Explorer from outside Representative Hortman’s home.

The firm says it offers only armed security. “If you are looking for unarmed guards, please work with another service to meet your needs better,” the website says.

Mr. Boelter’s public professional history is varied.

State reports and his LinkedIn profile indicate that he was recently a general manager of a 7-Eleven in Minneapolis and, before that, had worked as the general manager of a gas station in St. Paul. A report in 2017 listed him as an executive at an energy company.

More recently, he had said on LinkedIn that he was the chief executive of a company called Red Lion Group, in the Democratic Republic of Congo, dedicated to creating “good jobs for local people,” according to its website.

Mr. Boelter has delivered several sermons at a church in the Democratic Republic of Congo. In a video of one that was posted online, he appeared to criticize gay and transgender people.

“There’s people, especially in America, they don’t know what sex they are,” he said. “They don’t know their sexual orientation, they’re confused. The enemy has gotten so far into their mind and their soul.”

In the sermon, he said he had given his life to Jesus as a teenager and had been blessed with five children.

In a video posted online, seemingly for an educational course, Mr. Boelter said he had picked up work at funeral homes to help pay his bills.

It was not clear when the video was uploaded, but Mr. Boelter said he worked six days a week for two funeral homes in the Minneapolis area. At one, he said, he sometimes helped to remove bodies from crime scenes and would work with police officers and death investigators.

A spokesman for Des Moines Area Community College, in Iowa, said Mr. Boelter took classes in the school’s mortuary science program, an online program, in 2023 and 2024.

The website for Mr. Boelter’s security company makes expansive claims about his work experience, which could not immediately be verified, including that he had been “involved with security situations” in the West Bank and Gaza Strip and that he had worked for “the largest U.S. oil refining company, the world’s largest food company based in Switzerland and the world’s largest convenience retailer based in Japan.”

I.R.S. tax forms show that Mr. Boelter and his wife once led a Christian nonprofit called Revoformation Ministries. An archived version of the group’s website described Mr. Boelter as becoming an ordained minister in 1993.

Mr. Boelter, the site said, had traveled previously to violent areas “in the Gaza Strip and West Bank,” the site said, and had “sought out militant Islamists in order to share the gospel and tell them that violence wasn’t the answer.”

In November 2018, Mr. Boelter urged his followers on LinkedIn to vote in that year’s election, saying he had been to countries where people could not elect their leaders and that were “not places that anyone of us would want to live in.”

“I am very big on just telling people to be a part of the process and vote your values,” he wrote, “and be part of this adventure we are all a part of living in the United States of America.”

“I think the election is going to have more of an impact on the direction of our country than probably any election we have been apart of, or will be apart of for years to come,” he continued.

One of the victims on Saturday’s attacks, Ms. Hortman, ran successfully for re-election that year.

Julie Bosman, Kevin Draper, Adam Goldman, Bernard Mokam and Jay Senter contributed reporting. Jack Begg and Kitty Bennett contributed research.

She played a key role in passing a trove of bills during the 2023 session, when Democrats held a slim majority in the Legislature, including legislation that expanded abortion rights, legalized recreational marijuana and required employers to offer paid family and medical leave.

This year, under Ms. Hortman’s leadership, Democrats in the House boycotted the early weeks of the legislative session amid a fight for control of the chamber. Voters last year left Democrats and Republicans with an equal number of seats in the House, but challenges to two of the elections won by Democrats created a period of uncertainty around which party would control the chamber.

When those challenges were settled, Ms. Hortman agreed to let the top Republican in the House, Representative Lisa Demuth, serve as speaker.

Colleagues have long praised Ms. Hortman’s work ethic, negotiation skills and pragmatism.

Jerry Gale, Ms. Hortman’s campaign manager, said in an interview that she was a tireless campaigner who was passionate about recruiting fellow Democrats to run for office.

“She had a vision of what she wanted the state to be like, and she knew it was going to take a lot of work,” Mr. Gale said.

As the political rhetoric in the state grew more acrimonious in recent years, Mr. Gale said, Ms. Hortman worried about her safety.

“I think it did cross her mind at times on the campaign trail,” he said. Her own style was not combative, however. On the campaign trail and in the Capitol, Ms. Hortman kept her remarks short, to the point and civil, he said.

Ms. Hortman was married with two children, according to her state legislative biography. Her husband, Mark, was also shot and killed on Saturday.

Sen. John A. Hoffman has served in the Legislature since 2013. Before being elected, he served as a member of the Anoka-Hennepin School Board for several years.

Gov. Tim Walz of Minnesota said the Hoffmans had both undergone surgery. “We are cautiously optimistic that they will survive this assassination attempt,” he said.

Mr. Hoffman, 60, was born in Casper, Wyo., and formerly made a living as a marketing and public relations professional. He and his wife, Yvette, have a daughter. They live in Champlin, a suburb north of Minneapolis. His home address was published on his biographical page on the Senate’s website.

Mr. Hoffman chairs the Senate’s Human Services Committee. He is a fourth-term senator, and won his most recent election by 10 percentage points.

“A hallmark of my approach is collaboration across the aisle,” Mr. Hoffman wrote in a letter to constituents ahead of last year’s legislative session. “I firmly believe that the path to progress for our state involves considering input from all perspectives, regardless of which party holds the majority.”

On his campaign website, Mr. Hoffman said he was particularly proud of his efforts to make it easier for people with disabilities to work. He also described himself as a conscientious steward of taxpayer dollars.