NEW YORK — The mayor of New York castigated a police sergeant Wednesday for killing a mentally ill, 66-year-old woman in her home, saying her death was ‘‘tragic’’ and ‘‘unacceptable’’ and her shooting violated department policy.

‘‘Deborah Danner should be alive right now, period,’’ Mayor Bill de Blasio said at a news conference. ‘‘If the protocols had been followed, she would be alive. It’s as simple as that.’’

Officers were responding to a 911 call about an emotionally disturbed person around 6:15 p.m. Tuesday when they encountered Danner in her seventh-floor apartment in the Bronx, police said.

Police had been called to Danner’s home several times before to take her to the hospital during psychiatric episodes, the mayor said. Each of those times, she was taken away safely.

This time, something went wrong, the mayor said.

Sergeant Hugh Barry, an eight-year veteran of the force, persuaded Danner to drop a pair of scissors she had been holding, but when she picked up a baseball bat and tried to strike him, he fired two shots that hit her torso.

Danner is black. Barry is white.

Criticism of the shooting came almost immediately.

The New York City Police Commissioner James O’Neill told reporters Wednesday that his department ‘‘failed.’’

‘‘That’s not how it’s supposed to go,’’ O’Neill said. ‘‘It’s not how we train; our first obligation is to preserve life, not to take a life when it can be avoided.’’

The head of the police union representing sergeants, Ed Mullins, said the sergeant was justifiably defending himself.

‘‘We could be sitting here talking about how a 66-year-old . . . fractured [the officer’s] skull,’’ Mullins said.

The state attorney general’s office said it’s determining whether the shooting falls under its jurisdiction.

Assistant Chief Larry Nikunen said the sergeant was equipped with a stun gun. Police are investigating why he chose not to use it.

Associated Press