By Bernie Woodall

(Reuters) - A 23-year-old white man was arrested on Tuesday and will be charged with murder in the shooting deaths of two black men in Baton Rouge, Louisiana, authorities said.

Kenneth Gleason is accused of carrying out the killings on Sept. 12 and Sept. 14. Local media reported that police have said the killings may be racially motivated, but officials would not confirm that.

In both incidents a motorist opened fire on a pedestrian, said Parish of East Baton Rouge District Attorney Hillar Moore. Once the victims were on the ground, Moore said, the assailant got out of the car and shot them again several times.

Moore said prosecutors may seek the death penalty for Gleason if he is convicted.

But Moore said that even if the killings were determined to be racially motivated, it was unlikely Gleason would also face hate crime charges.

"You can't kill him twice," Moore told reporters at a news conference on Tuesday, saying such a charge was unnecessary in a death penalty case.

Baton Rouge Police spokesman Sergeant L'Jean McKneely would not say if the killings were racially motivated, but added, "We're not completely closed off to that."

Interim Baton Rouge Police Chief Jonny Dunnam noted the city has suffered racial turmoil in the past year or so.

In July 2016, a 37-year-old black man, Alton Sterling, was killed while scuffling with two police officers outside a convenience store. In May, the two officers were spared federal charges but still face a state investigation.

Twelve days after Sterling's death, a 29-year-old black man opened fire on Baton Rouge police, killing three officers before being fatally shot himself.

If police had not been able to bring "a swift conclusion" to last week's killings, Dunnam said, "(Gleason) could have potentially created a tear in the fabric that holds this community together."

McKneely would not comment when asked about reports that Nazi and satanic literature had been at the house where Gleason lived with parents outside Baton Rouge.

Gleason was detained on Saturday by a Baton Rouge police officer who recognized him from the description of the shooter driving a red car. Had Gleason not been arrested, said Dunnam, "this killer probably would have killed again."

Gleason will also be charged with shooting into an occupied residence near his parents' house. Moore said the homeowners were black. No one was injured in that Sept. 11 incident, he said.

(Reporting by Bernie Woodall; Editing by Daniel Wallis and Tom Brown)