Mr. Nigro said of the father, “I believe he acted very courageously and tried desperately, and hopefully it didn’t cost his life, too.”

Neighbors across the street called 911, and firefighters arrived two minutes and 40 seconds later. They confronted a home that was engulfed, Mr. Nigro said.

Two younger teenagers asleep in a back bedroom on the first floor, one of them a cousin of the Azan children, escaped out a side door with less serious injuries. They heard a smoke detector alarm and yelled to alert other members of their family, Mr. Nigro said. They were taken to Maimonides Medical Center.

The teenagers helped lead fire marshals to the cause when they told them that the menorah had been left burning after they went to sleep and that they saw the fire start nearby. Investigators recovered remnants of the broken menorah.

Investigators had not found other smoke alarms beyond the one that activated on the first floor. The Fire Department recommends that people install them on every floor of a home.

Five or six firefighters were injured, though none seriously, officials said.

“Over the last couple days, several other major fires have caused many injuries — some very serious — and displaced others from their homes,” Mayor Bill de Blasio said in a statement. “During the holiday season, we all need to be cautious with decorations, electric lights, candles, space heaters and other items.”

Two years ago, seven children were killed nearby when a hot plate warming food for the Sabbath started a fire in a family home. Mr. Azan had posted about it on Facebook.