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By The Associated Press

A Cuban law that bars anyone born on the island from returning by ship is discriminatory and should be eliminated, U.S. Secretary of State John Kerry said Thursday.

Kerry said the policy discriminates against Cuban-born citizens and immigrants and should be eliminated if Cuba's communist government is dedicated to having a full and normal relationship with the rest of the world.

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"The United States government will never support, never condone discrimination, and the Cuban government should not have the right to enforce on us a policy of discrimination against people who have a right to travel," Kerry said in an interview with CNN en Espanol and the Miami Herald.

Cruise line Carnival Corp. has denied ticket sales to Cuban-Americans because of the law, saying it has to comply with the visa, entry and exit policies of every country its ships visit. But the company said it has lodged a request with the Cuban government to change the ship policy.

Related: White House Eases Restrictions on Cuba Travel, Transactions

Two Cuban-Americans are suing Carnival Corp., claiming their civil rights were violated by the policy, which only applies to travel by ship, not other modes of transportation to Cuba.

Kerry stopped short of saying Carnival should cancel its planned route to Cuba, but said that "Carnival needs to not discriminate."

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The United States also has a complicated set of entry and immigration standards that aren't the same for people of every nationality.

Kerry was in Miami meeting with members of the Cuban-American business community.

Air Force One carrying U.S. President Barack Obama and his family flies over a neighborhood of Havana as it approaches the runway to land at Havana's international airport on March 20, 2016.Alberto Reyes / Reuters

The United States and Cuba began normalizing diplomatic relations in late 2014 after more than a half-century of estrangement. Since then, both countries have reopened their respective embassies in Washington and Havana, and last month President Barack Obama became the first sitting U.S. president to visit the island nation in nearly 70 years.

But the decades-old trade embargo also still remains in place and can't be abolished without approval from Congress.

Kerry also said that Cuba needs to continue to address human rights reforms, among other changes, before the embargo is likely to be lifted.