NEW YORK — The police officers who fatally shot a knife-wielding man after he escaped arrest in Times Square on Saturday afternoon did what they were trained to do, city officials and experts on police procedure said Sunday.

Two officers fired a total of 12 shots at the man, Darrius H. Kennedy, after he ignored their orders to drop the long kitchen knife he had been waving as he skipped backward down Seventh Avenue, frightening the tourists wandering around on a summer day, police officials said. At least seven of those bullets hit Kennedy, the police said.

Raymond Kelly, the chief of the New York Police Department, said he thought ‘‘the police responded appropriately’’ and that the number of rounds the officers fired was not unusual. Police officials said officers tried six times to subdue Kennedy with pepper spray without effect. None of the officers at the scene had a Taser or other type of stun gun, the police said.

Mayor Michael R. Bloomberg agreed with Kelly, saying the officers ‘‘probably acted in responsible ways’’ in trying to stop ‘‘somebody who must have been mentally deranged.’’ He added that ‘‘taking a knife and going after other people, particularly police officers, isn’t something that a sane person would do.’’

Police officials said they did not know whether Kennedy, 51, had a history of mental troubles. But they did say that in October 2008, he was taken to Bellevue Hospital for a psychiatric evaluation after he was found knocking over garbage cans in Times Square.

A month later, in November 2008, Kennedy was arrested near Lincoln Center after he threatened to harm police officers with a screwdriver when they tried to stop him from harassing drivers on Broadway, Browne said.

Saturday’s episode sent tourists running for cover (or their cellphone cameras), but nobody other than Kennedy was in danger of being shot, Browne said.