The Cuban government on Friday also hinted at its next move: the possibility of allowing Cuban-born people to travel to the island aboard recreational boats. That authorization, the government said, would come gradually and when circumstances are right.

Cuban-Americans in Miami who support engagement with Cuba have long envisioned the possibility of taking their own boats to the island, which is 90 miles away from Florida, to visit family.

Friday’s decision is significant because the Cuban government has long been wary of sea travel between the United States and Cuba. For decades, Cubans have fled the island by raft and rustic boats, something that continues today. The government also feared that allowing Cuban citizens to travel by sea would make it easier for hostile Cuban-Americans to enter the country and to undermine the government.

In 1980, after tensions in Cuba escalated as the economy plummeted, Fidel Castro allowed boats from the United States to pick up Cubans in the port of Mariel. More than 125,000 Cubans left the island by boat. Most of them were picked up by relatives, friends or recruits from Miami.

The Cuban government stressed that all passengers and crew members entering or leaving Cuba must have valid documents to do so. It also needled the United States, pointing out that American law continues to restrict American tourist travel to Cuba, although regulations have been eased.

The uproar, which Carnival did not anticipate, began this month when Cubans in Florida tried to buy tickets for the weeklong voyage. Carnival agents refused to book them on the cruise, saying that because they were Cuban-born, the Cuban government barred them from entering the country by sea.

In subsequent talks, the company and the Cuban government tried to find a resolution. This week, Carnival, which is based in a Miami suburb and is well-versed on local sensitivities about Cuba, faced a class-action lawsuit by Cuban-Americans and harsh words from political leaders who expressed outrage that an American company would discriminate against American citizens. Carnival initially delayed the trip, but remained optimistic.