A British passenger who disappeared from the world's biggest cruise ship in waters near Mexico can be seen jumping overboard in CCTV footage, the cruise line said.

The 30-year-old man, who has not been named, went missing from the Allure of the Seas as the ship sailed from Florida to Cozumel - an island south of Cancun.

Video footage shows the passenger - who dropped from the balcony in his stateroom - "intentionally went overboard" and "did not fall", the Royal Caribbean International cruise line said.

The assessment of the CCTV images appears to contradict a report from another traveller who claimed to have seen the man falling over railings at 12.10pm (7.10am local time) on Friday.

The Mexican navy and coastguard were later drafted in to assist with the search.

The Allure of the Seas - which can carry up to 5,400 passengers - boasts a park with more than 12,000 live plants, a zipline, a theatre, a casino and a nightclub. It left Fort Lauderdale in Florida on Sunday for a seven-night trip.

Royal Caribbean International said the ship had been fully chartered by Atlantis Events, described on its website as "the largest company in the world dedicated to creating unique vacations for the gay and lesbian community".

Multiple public announcements were made on the ship after the passenger went missing before a complete search of the vessel was launched in an effort to locate him.

"When the guest did not respond to the pages and was not found onboard, the captain alerted the local authorities of the situation," a spokesman for Royal Caribbean International said. "A review of the ship's closed-circuit camera footage observed the 30-year-old British male guest going over the balcony railing in his stateroom on deck 11. Our care team is providing support to the guest's family and our thoughts and prayers are with them," the statement said.

A spokesman for the Foreign Office said: "We are aware that a British national has been reported missing in Mexico. His family have been informed and we are providing consular assistance."