Surgery was successful for a Covington officer shot in the head while responding to a shoplifting call at a Walmart, police said Thursday morning.

Officer Matt Cooper underwent surgery Wednesday afternoon to relieve pressure on his brain. A bullet is still lodged against his carotid artery at the base of his neck.

MORE: Wounded Covington officer 'doing well' after surgery

“Officer Cooper had a restful night as the surgery to reduce the swelling seems to have been successful,” Covington police said on Facebook. “He's responding to questions by the squeeze of a hand. Matt is continuing to fight and his progress is impressive.”

Cooper’s condition is “obviously serious,” but his fellow officers remain hopeful the 34-year-old married father of two young children and Army veteran will pull through.

RELATED: Prayers are working': Wounded Covington officer mouths 'I love you' to wife

Covington police officer Matt Cooper was shot between the eyes, authorities said.

He has been in the hospital since Monday after he was shot pursuing a shoplifting suspect from a Walmart on Industrial Boulevard. Channel 2 Action News reported Cooper was hit between his eyes, and the bullet traveled down to his carotid artery, clotting his blood and saving his life.

MORE: Covington police officer shot near Walmart; 1 person dead

He was flown to WellStar Atlanta Medical Center in serious condition and moved to Grady Memorial Hospital on Tuesday. The hospital is conducting a CT Scan on Cooper every four to six hours, according to police.

“Thousands of you from all over the country continue to reach out to us to show support for the Cooper family.” police said on Facebook. “Words cannot express how touched we all are.”

A message of support is displayed on the Corey Airport Advertising Tower on the Downtown Connector. The digital billboard, which reads “PRAY for Ofc. Cooper,” is near Grady.

And a number of fundraising campaigns and events to support Cooper and his family have cropped up since he was wounded. The police department’s annual Fuzz Run on Saturday is being held in his honor.