MEXICO CITY (Reuters) - Mexico will free 14 Cuban migrants rescued by its navy this month and will give them permanent residency, a Mexican immigration official said on Monday.

The Cubans were intercepted off the Yucatan peninsula badly sunburned and dehydrated after three weeks adrift at sea, and Mexico's government said they would likely be deported. They were without food and survived by drinking rain water.

The 14 and another 18 Cubans left Manzanillo in eastern Cuba on Aug. 7 in a homemade boat, relatives of the survivors told Reuters. The boat's motor broke down after two days and the passengers rigged a makeshift sail.

Relatives said as many as 15 passengers died during the voyage, and their bodies were thrown overboard. Two more died after being rescued.

The Mexican immigration official said the 14 were being released on humanitarian grounds. The decision comes just days after Mexico's foreign minister visited the Communist-run island.

"Cuba did not recognize its citizens as such, so Mexico will give them a month to regularize their legal situation in the country," a spokeswoman for the Mexico's migration department INAMI said.

"They will remain in Mexico as legal residents while they wait for their permanent residency, which they are being given for humanitarian reasons," she said.

Mexico's foreign ministry had no immediate comment.

One other rescued passenger, who had a relative living in Mexico, was released earlier and is now in the United States.

"It's a huge relief," said Jose Caballero, husband of Maylin Perez, one of the women detained in Chetumal, in southern Mexico. "I haven't been able to eat. It's been a crazy few weeks. I was so worried they would be sent back to Cuba. If they did that I knew my wife would try and leave again."

Caballero took the same route by sea from Manzanillo in December, reaching Central America, before taking a bus to the U.S. border. He spoke to Reuters by phone from Texas where he now resides.

"I spoke to my wife this morning. She is happy. Now we just want to get our children out of Cuba," he added, referring to their son and daughter, aged eight and four, back in Manzanillo, where they are being looked after by relatives.

Under the "wet foot, dry foot policy" of the United States, Cuban migrants who make it onto U.S. soil are allowed to remain while those intercepted at sea are turned back.

Cubans seeking to flee the communist-run island are heading in increasing numbers to Central America or southern Mexico and then making a long journey overland to reach the United States.

U.S. authorities say 16,200 Cubans arrived without visas at the border with Mexico in the past 11 months, the highest number in a decade.

(With reporting by Nelson Acosta in Havana and David Adams in Miami; Editing by Simon Gardner and Steve Orlofsky)