In the meantime, he urged calm.

“This is a city in prayer,” he said. “People are just praying and asking for peace and comfort for the Bolton family and for all the men and women who have suffered the loss of a brother.”

Mr. Wharton also said that he had received a call from the White House on Sunday night.

“They are very much aware of what has taken place here and they are standing by to assist in any way they can,” he said.

Mr. Wilbourn was on supervised release in connection with a federal court sentence on a bank robbery charge, Director Armstrong said.

Sean Bolton was a veteran of the United States Marine Corps who served in Iraq, Director Armstrong said, and he joined the Memphis Police Department in October 2010.

Director Armstrong said that Officer Bolton was riding alone in his patrol car on Saturday night when he was shot and that after the suspect fled the scene, a nearby civilian used the officer’s radio to call in the shooting. Officer Bolton was taken to the Regional Medical Center near downtown Memphis in critical condition, and he later died there.

Director Armstrong said it was the third time in four years that a Memphis police officer had been fatally shot in the line of duty. Officer Timothy Warren was killed in July 2011 while responding to a shooting at a DoubleTree hotel in downtown Memphis. In December 2012, Officer Martoiya Lang was killed while serving a warrant in East Memphis.

The investigation into the killing of Officer Bolton comes as the Tennessee Bureau of Investigation is reviewing the fatal shooting of an unarmed man by a Memphis police officer on July 17. Officer Connor Schilling, 26, said he shot Darrius Stewart, 19, after Mr. Stewart attacked him with his handcuffs. Mr. Stewart had been riding in a car that was stopped for having a broken taillight, and was placed in the back of Officer Schilling’s police cruiser while the officer checked for warrants, the police have said.

Mr. Stewart’s family said that he had never been arrested and that the police had mistaken him for someone else.