Two suspects in an armed robbery that preceded the shooting of a Mississippi police officer were in custody early Monday, authorities said. 

Clarksdale Mayor Bill Luckett told the Associated Press that one of the suspects was brought in for questioning by his father Sunday afternoon. The second suspect was taken into custody at around 4 p.m. local time.

Both men are suspected of having robbed a convenience store four blocks from the site where Clarksdale Police Cpl. Derrick Couch was shot Saturday night.

Couch was in critical condition at the area's top trauma center, Regional One Health in Memphis, Tennessee, nursing supervisor Vivian Crawford said Sunday. Luckett said Couch is on a ventilator, has lost one eye, and the bullet remains lodged in his brain.

The mayor said surveillance video from a nearby law office shows Couch's patrol car approaching two men, one of whom runs.

"I'm not sure if Officer Crouch saw [one of the suspects] run or not," Luckett said. "Then you see the officer's lights turn and illuminate the second guy, who's walking. He walks with a noticeable limp, which is telling" because a video of a robbery last month at the same store, the Corner Grocery, shows a man with a limp.

The other man shot Couch after the officer got out of his car and approached the suspect, apparently to question him. 

"I've seen the video. It's harrowing," Luckett said. "As soon as the officer approached him, he just swung around and, bam!"

Neither suspect in custody had been identified by authorities. Both are African-American, as is Couch. Luckett said officers with a search warrant found "telling evidence" at the family home of the man whose father brought him to the station.

He said Couch is a veteran officer in his mid-30s, and worked for the Tunica County Sheriff's Office before coming to Clarksdale, where he was a narcotics officer until recently. He is married and has one or two children; other relatives live in Southaven, the mayor said.

"This is not a homicide yet. It would be our first this year if it turns into one," Luckett said. "I can't remember an officer in Clarksdale shot by a suspect."

The Associated Press contributed to this report.