The mystery surrounding the plane that vanished in the Caribbean grew Tuesday as the airline suggested the aircraft carrying 11 passengers may have been commandeered and the Coast Guard insisted it vanished over the water.

The U.S. Coast Guard was searching near the Turks and Caicos Islands for the missing aircraft, which sent out a distress call shortly before disappearing from radar.

Bad weather in the area was causing large swells and low visibility, making the quest difficult.

Aviation officials gave conflicting reports on the plane's origin, destination and whether it was considered stolen, hijacked in flight or lost over international waters.

"That plane apparently was stolen," an employee from Linea Area Puertorriquena Inc. (Puerto Rican Airline), who referred to herself only as Lara, told FOXNews.com.

She said the company was notified of the plane's disappearance Tuesday morning.

The twin-engine aircraft that vanished, a Britton-Norman Islander, could have been seized on the ground in the Dominican Republic, according to the carrier.

The company's owner, Luis Perez, said the plane was for sale. He planned to report it as stolen.

The United States Coast Guard denied that the aircraft vanished on the ground.

"It was over the water when they disappeared — that’s why we were notified," Coast Guard Petty Officer Barry Bena told FOXNews.com.

Bena said the plane, a multi-engine Britton-Norman Island that normally seats 18 people, simply "dropped off the radar" Monday afternoon.

The plane was initially said to be en route to New York, but the Federal Aviation Administration told FOX News that may not be true.

Jose Tomas Perez, director of the Dominican Civil Aviation Institute, said the aircraft sent an emergency signal before disappearing from the radar 35 minutes after taking off from the Dominican Republic at about 3:30 p.m. Monday.

Perez said the plane was heading to the Turks and Caicos Islands but never arrived. Providenciales police Sgt. Calvin Chase said airport authorities are still trying to locate records to determine whether the plane ever landed in Turks and Caicos.

But the FAA said the plane disappeared shortly after taking off from Providenciales in the Turks and Caicos. Spokeswoman Kathleen Bergen said the plane's destination was not immediately known.

"There's still a lot of unanswered questions here," Bergen said.

A U.S. Coast Guard spokesman, Nick Ameen, said rescuers searching for the plane were told it was expected to refuel in the Turks and Caicos.

Relatives of those missing told the U.S. Coast Guard that the passengers were ultimately trying to reach New York, Petty Officer Barry Bena said.

Coast Guard officials and others were searching the Atlantic Ocean but have not found any wreckage, Ameen said.

The Dominican aviation official, Jose Tomas Perez, initially identified the owner as Atlantis Airlines.

FOXNews.com's Rita Cant, FOX News' Harris Faulkner and The Associated Press contributed to this report.