A man attacked four girls with a meat cleaver in a Brooklyn home on Sunday morning before he was shot by the police, who rushed to the house after one of the injured children called 911, the police said.

All four girls, ages 8, 11, 13 and 16, have serious slash and stab wounds but are expected to survive, Jessica Tisch, the police commissioner, said at a news conference near the home in the Bensonhurst neighborhood of Brooklyn.

The man, Longqian Chen, 49, who the police believe is related to the girls and was alone with them and a boy, was taken to a nearby hospital in critical condition, Commissioner Tisch said.

She praised the 11-year-old girl, who hid in a room to call 911, as well as the officers who kicked down a locked door to reach the children and police communications technicians who were able to track the phone the girl had used to identify the home’s address.

Those actions, the commissioner said, “absolutely saved the lives of the young girls.”

“This could have ended very differently,” she added.

It was unclear how Mr. Chen was related to the children and why he attacked them. The police had never received a report of domestic violence at the home, John Chell, the chief of department, said. But Commissioner Tisch said that, according to family members, Mr. Chen had a history of mental illness.