A missing elderly couple likely fell off a Carnival Cruise ship between Long Beach and Mexico, company officials have said.

A 90-year-old man and his 79-year-old wife were aboard the Carnival Paradise when it departed Monday from Long Beach, but they could not be found when it returned Friday morning.

Miami-based Carnival said the couple's cabin door was double-locked from the inside with a "Do Not Disturb" sign on the handle. Their belongings remained inside, and the door leading from the cabin to the private balcony was unlocked.

The couple were last seen on Tuesday evening, and a Carnival spokesperson reportedly told the Press that they did not know if the pair disembarked in Catalina or Ensenada during the five-day Mexico cruise.

The FBI has been talking to passengers and crew and the Coast Guard has been conducting a search by plane.