The New York Times, citing an unidentified law enforcement official, said the letters were long and rambling and appeared to claim responsibility for the blast at the recruiting station in the center of Times Square. They included photographs that showed a person standing in front of the kiosk.
The FBI has joined the investigation and is examining the letters, which arrived Thursday.
The early morning blast damaged the door and window of the recruiting station. New York Police Commissioner Raymond Kelly said a witness saw a bicyclist wearing a hooded jacket near the recruiting station just before the explosion.
Kelly said the simple bomb was in a U.S. Army ordnance container. Investigators were checking to see whether there was any link between Thursday's explosion and two explosions at consulates -- the Mexican consulate in October and the British consulate in 2005.
Subway service through Times Square, one of the city's major mass transit hubs, was suspended for some time and streets were closed to traffic for more than two hours until police were sure no other bombs had been placed.
"Any time there is an explosion of a bomb we have to be concerned, regardless of where it is," Kelly said. "Certainly Times Square is the crossroads of the world, and we are concerned about that."