LAKE CITY, Minn. — An all-day standoff ended when authorities entered a house Monday and found a body believed to be that of a man who shot and critically wounded a police officer in southeastern Minnesota.

SWAT officers surrounded the home in Lake City, and nearby schools were locked down after a man shot the officer, then retreated into the house. When authorities entered the house and found a body believed to be that of the shooting suspect, they advised schools to end their lockdown and transport students home.

Police identified the wounded officer as Shawn Schneider, 32, who has been employed at Lake City since 2003. He remained in critical condition Monday evening after being shot in the neck and head.

“It’s been a very sad and unfortunate day for our community,” Lake City Mayor Jerry Dunbar said at an evening news briefing.

Police Chief Gary Majchrzak said the shooting happened after 8:30 a.m. when two officers went to a house for a reported domestic situation involving a handgun. When they arrived at the house, a man shot one of the officers.

Authorities identified the suspect as Alan Sylte Jr., 25, of Hager City, Wis. He does not live in the house but was apparently involved in a domestic situation with a woman there. The woman left the residence before the officer was shot, and it was believed she was unharmed.

The wounded officer was taken to St. Marys Hospital in Rochester, where Majchrzak said he was in critical condition.

Majchrzak said authorities believed Sylte went back into the house after the shooting. But authorities did not have contact with him, so they warned residents he is considered armed and dangerous. Officials believed he had a small-caliber handgun and fired two shots at the officer.

Authorities had no immediate details on the nature of the domestic situation.

Schools in Lake City were locked down all day. As of 4 p.m. — after the school day ended — students were still being kept inside. Evening school activities, including a winter band concert, were canceled.

Fourth-grader Phillip Leonard, 9, and his sixth-grade brother, Hayden Leonard, 11, said the day was a mix of emotions

“It was kind of scary because you didn’t know what was going,” Phillip Leonard told the Post-Bulletin of Rochester. “They made us sit in the classroom for a long time. They said it was a lockdown, but that was all.”

The boys were picked up with their sisters about 7:15 p.m.

Hayden Leonard said they spent the entire time in the classroom and needed an escort to the bathroom. Lunch was delivered to the classroom. The choice was a sandwich or a bagel.

“We don’t feel comfortable releasing kids … we don’t know if all of our neighborhoods are safe,” said Superintendent Craig Junker. “The safest place for our children to be is in our schools.”

Junker said the lockdown would continue until law enforcement gave the all-clear. About 1,200 students in the school district were affected, including students at Lincoln High and Middle schools and Bluff View Elementary. St. John’s Lutheran School was also locked down. When the lockdown ended, hundreds of students filed out of the schools into the hands of relieved parents, the Star Tribune of Minneapolis reported.

Sylte has a short court record in Wisconsin, including charges of battery and disorderly conduct in 2006, but those charges were dismissed.

The Minnesota Bureau of Criminal Apprehension will investigate the shooting. The Wabasha County medical examiner will positively identify the body of the man found in the house.