Carnival Corp said on Tuesday a majority of its ships' itineraries were unchanged, despite a surge in Omicron coronavirus cases that has threatened to stall a recovery in the cruise industry.

The world's largest cruise operator, however, said a few destination ports were reviewing their protocols and processes due to the fast-spreading new variant.

Many passengers and reports, including those from CNN and Euronews, said authorities of a few ports in the Caribbean, Puerto Rico and Mexico disallowed passengers from cruise ships that were carrying active COVID-19 cases to disembark.

"Looks like my cruise this Friday is a cruise to no where," wrote one Reddit user on a Royal Caribbean forum late Monday.

Carnival said on Monday it would find an alternative destination should it be forced to cancel a port. Royal Caribbean Group did not respond to a Reuters request for comment, while Norwegian Cruise Line Holdings Ltd declined to comment.

"The cruise lines' reaction to the substantial increase in COVID-19 cases caused by the Omicron surge is largely hit or miss," said James Walker, a Miami-based maritime lawyer.

Carnival's shares were up 1%, while those of Norwegian Cruise and Royal Caribbean were largely flat.

The Omicron variant has sparked concerns that the U.S. health officials may reintroduce a temporary ban on cruising, just months after U.S. cruise operators resumed guest operations.