A white man with a history of violence shot dead two African American customers at a grocery store in Kentucky and was swiftly arrested as he tried to flee, police said Thursday.

They said it was too soon to say what prompted Wednesday’s shooting, responding to an earlier account from a witness that when confronted with another white man during the incident, the suspect said: “Whites don’t shoot whites.”

The Jeffersontown police chief, Sam Rogers, said: “I can’t speculate on motive at this time.” He said surveillance video showed the suspect tried unsuccessfully to enter the First Baptist church in Jeffersontown before he went to the Kroger grocery store. The church is headed by a black pastor and has a large African American membership.

The FBI announced that it “is evaluating the evidence to determine if there were any violations of federal law”.

Rogers also said the suspect, 51-year-old Gregory Alan Bush, apparently had a history of mental illness, as local news outlets have reported.

An arrest report says Bush walked into the store outside Louisville, pulled a gun from his waist and shot a man in the back of the head, then kept shooting him “as he was down on the floor”. The report says Bush then re-holstered his gun, walked outside and killed a woman in the parking lot.

Bush, 51, was jailed on a $5m bond Thursday on two counts of murder and 10 counts of felony wanton endangerment.

Ed Harrell was quoted by the Courier Journal of Louisville as saying he was waiting for his wife in the parking lot when he heard gunshots and grabbed his revolver. As he crouched down, he said he saw the gunman walk “nonchalantly” by with a gun by his side. He said he called out to ask what was going on, and the gunman replied: “Don’t shoot me. I won’t shoot you. Whites don’t shoot whites.”

At Thursday’s news conference, Rogers said police “are aware of that statement and are evaluating any factors that that may come into play with” it.

The local coroner’s office identified the victims as Maurice Stallard, 69, and Vicki Lee Jones, 67. Stallard is father of Kellie Watson, the chief racial equity officer for the Louisville mayor, Greg Fischer.

The mayor shared his outrage Thursday over what he called an “epidemic of gun violence” that “hit close to home”.