FORT LAUDERDALE, Fla. – Two men and a woman were rescued from a deserted island Tuesday after surviving on coconuts, conch and rats for 33 days, the U.S. Coast Guard said.

The Coast Guard spotted people waving flags Monday during a routine air patrol of the waters around Anguilla Cay, in a chain of islands between the Lower Keys and Cuba. The Coast Guard returned to drop water, food and a radio.

A helicopter crew picked them up Tuesday and flew them to the Lower Keys Medical Center. None of them appeared seriously hurt.

Lt. Mike Allert, the pilot of the rescue helicopter, said that the rescue was delayed until Tuesday because of bad weather, ABC News reported.

"Our rescue swimmer found them to be fatigued, dehydrated and showing definite signs of just being out in the elements for the extended amount of time that they were there," he said.

The Coast Guard said the trio was from Cuba. They told the helicopter crew their boat capsized in rough waters nearly five weeks earlier, and they were able to swim to the deserted island.

"Thanks to our aircrews diligently conducting routine patrols, we were able to spot people in distress and intervene," said Sean Connett, a command duty officer at the 7th Coast Guard District. "We were able to safely get everyone to a medical facility before the situation could worsen."

After the three were evaluated at the hospital, they were handed over to the U.S. Border Patrol, the Coast Guard said, and transferred to Immigration and Customs Enforcement.

Coast Guard Petty Officer 2nd Class Brandon Murray said it was remarkable that the three people survived.

"I cannot recall a time that we saved people who were stranded for over a month on an island," he said. "That is a new one for me."

The New York Times contributed to this report.