"Paramedics bringing someone from the plane/helicopter crash onshore at Pier 40. Cop cars/fire trucks everywhere," one tweeter wrote on Twitter, quoting the user "mikomercer."
Later, a large crane on a barge moved toward the debris field.
Bloomberg said this afternoon that the wreck of one aircraft had been found toward the New Jersey side of the river.
"We believe it is the helicopter," he said, "but the visibility is about two feet at a depth of 30 feet."
The second aircraft, believed to be a Piper Saratoga, was not initially located.
"Unfortunately, there's not a lot of rescue to be done here," Bloomberg said. "It's all recovery from this point on."
Air traffic controllers at Newark International Airport reported that they lost radar contact with the Piper airplane around noon, said Jim Peters of the FAA.
The Newark tower monitors air traffic on the part of the Hudson River where the accident occurred. However, planes and helicopters can fly that corridor below 1,100 feet under visual flight rules and bypass direct control by controllers. Such craft must "see and be seen," and it is their responsibility to avoid other aircraft.
Planes flying south, as this one was, are required to fly along the New Jersey side of the Hudson River.
New York Gov. David Paterson vowed to work closely with city and federal investigators to get to the bottom of the crash, which he called "a tragic accident."
"As we continue to monitor the progress of the recovery efforts, our hearts and prayers go out to the families of those who were on board each of these aircrafts -- both here in New York and in Italy," Paterson said in a prepared statement. "What began as a beautiful day with blue skies has turned into a day of darkness for those who lost someone they love today."
ABC News' Aaron Katersky, Dan Gura, George Sanchez and Stephanie Sy contributed to this report.