NEW YORK — Investigators sought answers Monday for why safety doors failed to close when fire broke out in a New York high-rise, allowing thick smoke to rise through the tower and kill 17 people, including eight children, in the city’s deadliest blaze in more than three decades.

A malfunctioning electric space heater apparently started the fire Sunday in the 19-story building in the Bronx, fire officials said. The flames damaged only a small part of the building, but smoke poured through the apartment’s open door and turned stairwells.