The 73-year-old victim, who is the building's landlord, remains at Nassau University Medical Center with second- and third-degree burns to 80 percent of his body.
The incident happened in front of a house that is rented to two families on 222nd Street in Springfield Gardens.
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Police say the package was sitting on the front stoop for a number of days.
The man picked up the round cylinder that police say was packed with black powder, and it exploded.
The name on the package was not anyone who lives at that address, investigators said.
NYPD Chief of Detectives Robert Boyce says the explosive was rigged to detonate when someone opened it. He says the blast left behind "substantial evidence."
One resident of the home saw the package for several days and even touched it.
"We didn't think nothing of it, my dad was actually holding it and he was like, 'is this for us?' and I said it's not for us," said Kathleen Toussint. "I said just put it outside and I guess they'll pick it back up, to whoever it needs to go to they'll find it. And the landlord came and he saw it during the week and I guess he realized it was still sitting there and he decided he wanted to open it I guess, and that's what happenped."
Police say there was no evidence of shrapnel, just black powder.
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"I saw a man lying in the grass he was actually on his knees and he was on fire," said Rick Thomas, a neighbor. "He was screaming out in pain, a lot of pain, he was engulfed, the flames engulfed his whole top half."
"When I got out there, there was a neighbor across the street they had ran to aid him and they put towels around him to put the fire out, and someone called 911, and the firemen were on the scene first," a neighbor said.
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The U.S. Postal Service released a statement:
"This matter is currently under investigation with law enforcement and we cannot provide further comment at this time."
The victim owns the home but does not live there.
Police didn't think the package had been sent through the mail.
(The Associated Press contributed to this report.)