Police officers in the Bronx burst in on a man who was beating his mother with a frying pan Sunday night and fatally shot him, the police said.

The woman, Kuan Balbir, was in critical condition with a fractured skull among other injuries and was likely to die, the police said.

A relative told investigators that the man, Satnam Singh, had a history of emotional problems. Mr. Singh was arrested in 2007 in Queens and was later convicted on charges of assault and resisting arrest, according to the police.

The authorities received a call on Sunday from another of Ms. Balbir’s sons, saying that he had not heard from his mother. When the officers went to Ms. Balbir’s apartment at 3055 Third Avenue around 11 p.m., they heard noises inside. The officers tried to enter and could not.

The super unlocked the door, which was chained shut, the police said.

Through the opening, the officers saw Mr. Singh standing over a woman, who was covered in blood and sitting on a couch, the police said. The woman was being struck repeatedly with a 17-inch frying pan.

“Oh, my God, he killed his mother,” the super said, according to the police.

The officers broke the door down, and three of them entered the apartment and told Mr. Singh repeatedly to drop the pan.

“We have multiple witnesses, including the super, who stayed in the hallway, who said that they heard the police tell the man to stop,” said Paul J. Browne, the Police Department’s chief spokesman.

Mr. Singh did not drop the pan, and he raised it as if to strike the woman again, the police said.

They said that one of the officers, who was standing next to the other two about 15 feet from Mr. Singh, fired two shots at Mr. Singh.

Mr. Singh staggered away from Ms. Balbir but then moved back toward her and raised the pan again to strike her, the police said.

One of the officers, a sergeant, fired at Mr. Singh once, and officer who had fired the first two shots fired two more.

Mr. Singh collapsed to the floor and was later pronounced dead at the scene by medical personnel. Investigators found three bullets in Mr. Singh’s torso and fragments of bullets in his right arm.

Ms. Balbir was taken to Lincoln Medical and Mental Health Center in critical condition. Her skull was fractured, she had bleeding in her brain, and a bone was sticking out from her left forearm, the police said.

The police did not release the names of the officers involved. However, Mr. Browne said that the officers all tested negative for alcohol and had no previous shooting episodes.