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The suspect, 45, was seen starting the fire in the five-story building at 41 Spring Street, near Mulberry Street, in the heart of NoLIta, around 6:40 p.m., the police said.

The man, whose name was not released by the authorities, fought with first responders, trying to stop them as they tried to battle the blaze, the police said. He was arrested and taken to New York Downtown Hospital with bruises. The mother and child were taken to a police station "in good health," said Paul J. Browne, the chief spokesman for the police.

The dead person was found on a third-floor fire escape, but the authorities said they did not know if the person lived in the building or even whether it was a man or a woman. The body was "burned beyond recognition," Mr. Browne said.

It took nearly 200 firefighters two and a half hours to bring the fire under control, fire officials said; the building has a Pinkberry shop on the ground floor and apartments above.

"We had an extraordinary amount of fire," said James Esposito, chief of operations for the Fire Department. It burned upward to the roof, destroying the interior staircases, so firefighters had to use fire escapes and ladders. "It was an extremely intense operation," Chief Esposito said. "The fire encompassed all the walls, all the floors," he said. "We have a partial collapse inside the building right now. It's essentially destroyed."

Seven firefighters and at least two other people were injured. A police officer broke his hand in the fight with the suspect.

William Bray, 25, a chef who lives a block away, said he ran into the street when he saw flashing lights coming from the building. "There were flames coming out of the second-floor window," he said. "Then, soon after, we began to see smoke billowing out of the third-floor windows."

He said he saw the suspect being led from the building in handcuffs. He was not wearing shoes, had blood on his shirt and a black eye, Mr. Bray said. He said he recognized him as someone who frequented the park opposite the building with a young son.