The bodies of two others who were on board the Learjet 35 were found. Two Coast Guard cutters, a helicopter and several boats and divers searched a debris field two miles northeast of Fort Lauderdale-Hollywood International Airport trying to locate the remaining victims.
The plane had just dropped off a patient at a South Florida hospital Tuesday night and had taken off from a private terminal at Fort Lauderdale-Hollywood International when it plunged into the water about a mile offshore, authorities said. The patient was originally picked up from Costa Rica before being dropped off in Florida.
The flight was headed to Cozumel, Mexico.
Mexico's Transportation Department said the plane was carrying pilots Jose Hiram Galvan de la O. and Josue Buend?a Moreno and passengers Fernando Senties Nieto and Mariana Gonzalez Isunza. Mexican officials did not specify which of the people's bodies were found.
A spokesman for the airport said the jet was carrying two pilots, a doctor and a nurse. The jet was run by AirEvac International. U.S. Coast Guard Chief Petty Officer Ryan Doss identified all four aboard as Mexican national citizens.
In a distress call, the pilot told the air traffic control tower, "We have an engine failure," and he requested permission to return to the runway.
"We're going to do a 180 and we're going to land," he says. A few minutes later, in response to the tower's instructions, the pilot said, "Mayday, mayday, mayday."
The Federal Aviation Administration says the plane went down approximately four miles northeast of the airport.
Albert Carson, director of operations for AirEvac International, said his company has sent documents to the Mexican consulate to try to identify the deceased, a process that continued Wednesday afternoon.
According to the company's website, AirEvac International's main bases of operation are in Mexico, Central America and South America and San Diego, Calif.
FAA officials warned of potential problems found in the Learjet 35 in June. A special bulletin states that maintenance workers found cracks in the control column on Learjet Model 35A (C-21A) airplanes. Five airplanes were inspected and all five had cracks in the area at the base of the column where it attaches to the floor.
But the concern was not deemed dangerous enough to warrant a further directive, according to the bulletin.
Overnight, rescuers hauled in wreckage from the plane and asked boaters to avoid the area for safety reasons.
The National Transportation Safety Board is investigating.
ABC News and the Associated Press contributed to this report.