The Army Corps of Engineers is being consulted about trying to pull the aircraft to the surface.
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The wreckage of the single-engine Piper was found in about 60 feet of water in the middle of the river, indicating it had drifted from the spot where it crashed, closer to New Jersey's riverbank, said the New York Police Department's top spokesman, Paul Browne.
The bodies of one person on the plane is still missing.
A suburban Philadelphia development executive, his brother and nephew and an Italian tourist group were killed in Saturday's crash in the busy skies of Manhattan. The helicopter was raised from the water on Sunday.
The divers Monday fought currents exceeding 3 knots. Silt reduced visibility to less than 6 inches in some places on the river bottom and was never better than a foot, said New Jersey State Police Lt. Albert Ponenti.
"It was a difficult dive due to the conditions," Ponenti said. "It's very risky to put divers in this river because of the currents, which can exceed the 3 knots you see on the surface, and because of the poor visibility."
The helicopter carried a pilot and the five Italian tourists, who have been identified through their fingerprints, said Italian Ambassador Giovanni Castellaneta.
Castellaneta said he had met with the medical examiner in New York and with relatives of the victims.
"Today the relatives were asking me, 'How it can be that a holiday in New York can become such a tragedy?"' Castellaneta said in Italian. He promised to find out and said, "We intend to keep that promise."
About a half-dozen relatives of the Italians were still in New York, including cousins and uncles, waiting to travel back with the bodies. A group of 10 tourists traveled from Italy, two to celebrate a 25th wedding anniversary.
"They are destroyed by pain," Castellaneta said.
Other members of the tourist group had gone on a helicopter ride a day before the crash and had planned to go again, he said.
"They told me that the day before, they had the tour on New York City and were very happy about the tour," Castellaneta said. "And they had booked another tour, but of course that was canceled."
Prosecutors in Bologna, Italy, on Monday opened a routine investigation into the crash after receiving a complaint from Codacons, an Italian consumers' group. The probe for multiple manslaughter and causing a disaster does not name any suspects.
National Transportation Safety Board chief Debbie Hersman said on NBC's "Today" show that investigators will eventually examine the aircrafts' structural integrity and will try to determine how the initial impact occurred.
She declined to speculate about the cause of the crash. The investigation is expected to take months.
Witnesses said the small plane approached the helicopter, which had just taken off from Manhattan's West Side for a 12-minute tour, from behind and clipped it with a wing. Hersman said the helicopter was gaining altitude when the two hit. Both aircraft split and fell into the river, scattering debris and sending weekenders enjoying the beautiful day running for cover.
The plane took off from Teterboro Airport in New Jersey shortly before noon. Hersman said it was not required to have a flight plan and did not file one. The plane was flying at about 1,100 feet, she said. Below that altitude, planes in that part of the Hudson River corridor are to navigate visually. Above that, they need clearance from air traffic controllers.
--- Hays contributed to this report from New York. Associated Press writers Sara Kugler and Maria Sanminiatelli in New York and Geoff Mulvihill in Hoboken, N.J., also contributed to this report.
