A man is being questioned by police in connection with the death of a woman burned alive in the lift of her New York City apartment building.

Police said a man smelling of petrol walked into a police station overnight and implicated himself in the killing.

The 47-year-old man, who had not been charged, said he had started a fire, a New York police department spokesman said. The man's identity was not released.

Doris Gillespie, 64, was ambushed in the lift of her Brooklyn apartment building on Saturday afternoon, doused with an accelerant and set on fire with a Molotov cocktail. The suspect had been waiting for her when the lift doors opened to the fifth floor of her apartment building in Prospect Heights,.

"It was apparent he knew she was on the elevator," police said.

The attack happened shortly after 4pm, lasted about a minute and was recorded by two video cameras, including one inside the small lift.

The video showed the lift doors opening to the floor where Gillespie's apartment was located and the assailant stepping in and spraying her.

Gillespie, who had grocery bags in her arms, turned about 180 degrees and then crouched in an attempt to protect herself, he said. But the man sprayed her directly in the face and continued to spray her "sort of methodically" over her head and parts of her body as the bags draped off her arms. She turned and retreated to the back of the lift.

Then the suspect pulled out a barbecue-style lighter, used it to ignite a rag in a bottle and then waited for a few seconds before using the flames to set her alight, causing smoke to fill the lift.

The man backed out as the woman fell to the floor of the lift and seemed to pause before tossing the bottle inside the lift on to the woman.

Police would not comment on the motive for the killing, but said the suspect knew the victim.

On Saturday night police released still images of a man in a black jacket, wearing what appear to be surgical gloves and with a white dust mask perched on his head like a pair of sunglasses. He is holding what appears to be a canister with a nozzle and spraying as he steps into the elevator.

Neighbours reported a fire in the building, unaware that the woman was burning alive in the lift.