They had few answers for the city at the news conference later in the day, citing the ongoing investigation.
The state trooper, who is in stable condition, and the two others who were injured, one of them critically, are being treated at a hospital.
In a statement, Governor Andy Beshear (Democrat) called the shootings “senseless acts of violence”.
At about 11.36am, the suspect allegedly shot a state trooper on Terminal Drive, a roadway on airport property, before fleeing on foot.
The suspect then allegedly stole a car, which officials tracked to Richmond Road Baptist Church. There were no injuries reported from the alleged carjacking, Lexington Police Chief Lawrence Weathers said.
At the church, three officers opened fire with their service weapons, Weathers said.
Those officers, who were not identified, will be placed on administrative leave pending the results of the investigation, in accordance with the police department’s policies, Weathers said.
Kentucky Attorney-General Russell Coleman (Republican) said that “violence invaded the Lord’s House”.
“The attack on law enforcement and people of faith in Lexington shocked the entire commonwealth,” Coleman said in a statement.
A spokesperson for the airport told the Washington Post that the facility had shut down for half an hour in the morning “out of an abundance of caution” but has since been fully operational with flights coming and going as expected.