The fire broke out Friday around 9 p.m. in the building on 351 East 84th Street near First Avenue.
Officials say two other people were injured in the fire - one serious and one minor injury.
Sources say the victim, a 76-year-old man, is a smoker, and believed to have started the fire.
He was later identified as Joel Beeler and was found with burns lying in his bed.
A woman was reportedly in the apartment with him at the time and noticed the fire too late to do anything.
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