Officers Mike Ringgenberg and Dustin Schwarze are now on standard administrative leave, the Minnesota Department of Public Safety's Bureau of Criminal Apprehension said in revealing the officers' names.
"The two Minneapolis police officers responded to a request for assistance from paramedics who reported an individual, now identified as Mr. Clark, disrupting their ability to aid an assault victim at that location," the bureau said in a statement.
"Minneapolis police have said that Mr. Clark was a suspect in the assault. At some point during an altercation that ensued between the officers and Mr. Clark, an officer discharged his weapon, striking Mr. Clark," state authorities said.
The state agency didn't say which officer fired shots.
State investigators looking into the shooting of Clark, 24, have obtained videos that show parts of the incident, but none show the entire event, an official said Tuesday.
Agents from the Bureau of Criminal Apprehension have gathered videos recorded by witnesses using cell phones, surveillance cameras at nearby apartments, a mobile police camera and an ambulance recorder. There might also be video from a camera at an Elk's Lodge, Drew Evans, the superintendent of the bureau, told reporters this week.
But there is no dashcam video from police cars or body camera video, Evans said.
Clark died Monday night of a gunshot wound to the head, the Hennepin County Medical Examiner's Office said in a preliminary report.
Authorities say they didn't find any weapons where Clark was shot early Sunday morning when police answered a call of a woman being assaulted by a man.
Evans said officials will wait for the autopsy report before revealing how many times Clark was shot. He said it would be weeks before the videos are disclosed publicly. Authorities don't want to influence potential witnesses, he said.
Evans said investigators found handcuffs at the scene and are trying to determine whether Clark was wearing them at the time he was shot.
Police have said Clark was not handcuffed when he was shot, but protesters have disputed that.
The FBI also is investigating the case.
Protests heat up
Protests outside a police precinct grew throughout the day and became increasingly tense after darkness fell.
Minneapolis police spokesman John Elder said officers deployed chemical irritants but protesters around the 4th Precinct also deployed a chemical irritant against police.
Officers fired two marking rounds at a man who threw bricks at officers, Elder said. No rubber bullets were used, he said.
Bricks and rocks thrown by protesters damaged police cars in the precinct lot, he said.
Officers were set up around the building to ensure the station is not breached by protesters.
Earlier in the day, police removed some of the tents of protesters who had been camping outside the precinct. Minneapolis Police Chief Janee Harteau said the Black Lives Matter demonstrators also were asked to move from an area in the building that citizens use to enter the station.
Shvonne Johnson, the assistant dean of students at St. Catherine's University, told CNN affiliate WCCO
she was inside the vestibule with students when officers came to get them out. The women were in the process of leaving when officers "charged at them," she told the station.
Some protesters threw rocks and bottles at officers, authorities said. Several patrol cars were damaged. Two people were arrested, officials said, one for throwing a bottle.