Nine people are presumed dead following the crash at 4am today (NZ Time).
Liberty Helicopters said the pilot was Jeremy Clark, 33, who had been living in New Jersey, the New York Times reported.
Mr Clark's aunt told One News his parents had gone to Auckland Airport this evening, hoping to travel to New York.
A Ministry of Foreign Affairs spokeswoman told NZPA it had not received a request for help.
It was believed Mr Clark's sightseeing helicopter, carrying five Italian tourists, was hit from behind by a small private plane carrying three people, including a child. Debris was scattered across the water and thousands of people on the waterfront were forced to scamper for cover.
A helicopter pilot refuelling on the ground at the Liberty Tours heliport saw the plane approaching the helicopter and tried to radio an alert to the pilots, police Commissioner Raymond Kelly said. The warning wasn't heard, or didn't happen in time.
"He radioed the accident helicopter and told him, `One-lima-hotel, you have a fixed wing behind you'," National Transportation Safety Board Chairman Deborah Hersman said on Saturday.
"There was no response."
The collision, which Mayor Michael Bloomberg said was "not survivable", happened just after noon (local time) and was seen by thousands of people enjoying a crystal-clear summer day from the New York and New Jersey sides of the river.
"First I saw a piece of something flying through the air. Then I saw the helicopter going down into the water," said Kelly Owen, a Florida tourist at a Manhattan park.
"I thought it was my imagination."
The two aircraft crashed just south of the stretch of river where a crippled US Airways jet landed safely in January. But this time there was no miracle.
"This is not going to have a happy ending," Bloomberg said.
The air accident, the deadliest in the New York City area since the 2001 crash of a commercial jet in Queens killed 265 people, also raised questions about the heavily trafficked river corridors for small planes on both sides of Manhattan.
Officials considered new restrictions for the aircraft after a 2006 small-plane crash killed New York Yankees pitcher Cory Lidle and his flight instructor.
Three bodies from Saturday's crash had been recovered before diving operations were suspended for the night, Hersman said. The helicopter's wreckage had been found but not the plane, she said.
Tides and low visibility were compromising the recovery operation, she said. She warned residents not to touch pieces of debris that were likely to wash ashore.
Witnesses described seeing a low-flying plane smashing into the helicopter, and then wreckage scattering. One of the plane's wings was severed by the impact.
The accident happened in a busy general aviation corridor over the river that is often filled with sightseeing craft on nice days.
Pilots have some freedom to pick their own routes, as long as they stay under 305m and don't stray too close to Manhattan's skyscrapers. The skies over the river are often filled with pleasure craft, buzzing by for a view of the Statue of Liberty.
Steve Riethof, a volunteer at the Aviation Hall of Fame in Teterboro, New Jersey, said Saturday that pilots headed for the Jersey Shore from Teterboro generally fly through Manhattan.
In January, the river was the scene of a spectacular aircraft landing that resulted in no loss of life after a US Airways flight taking off from LaGuardia Airport, in Queens, slammed into a flock of birds and lost power in both engines. The plane crash-landed in the river, and all 155 people on board were pulled to safety.
Liberty Helicopters, which runs Liberty Tours, expressed condolences to the victims in a statement Saturday and said it was cooperating with the National Transportation Safety Board.
Two years ago, a Liberty helicopter fell 152m from the sky during a sightseeing trip. The pilot was credited with safely landing the chopper in the Hudson and helping evacuate her seven passengers.
In 1997, a rotor on one of its sightseeing helicopters clipped a Manhattan building, forcing an emergency landing. No one was hurt.
