Senate Majority Leader Mitch Mcconnell, R-Ky., says Congress could block moves to normalize relations with Cuba. Pictured: McConnell talks to reporters July 8, 2015. Reuters/Kevin Lamarque

WASHINGTON (Reuters) -- The top Senate Republican said on Sunday that Congress is likely to block any nominee that President Barack Obama names as ambassador to Cuba and retain broad economic sanctions, even as Obama moves to establish diplomatic and economic ties with the Communist-run island.

Senate Majority Leader Mitch McConnell, interviewed on the "Fox News Sunday" television program, said the Senate is unlikely to confirm any U.S. ambassador to Havana nominated by Obama.

McConnell added, "There are sanctions that were imposed by Congress. I think the administration will have a hard time getting those removed. This is a policy that there is substantial opposition to in Congress."

Last December, Obama announced he would use his executive powers to move toward more normal relations with Cuba after a five-decade standoff.

Those steps have included establishing diplomatic relations, an expansion of some travel from the United States to Cuba, increasing the limit on remittances to Cuban nationals from those living in the United States and expanding some trade in goods and services.

But it would be up to Congress to allow normal travel and full trade.

Republicans control both the Senate and House of Representatives. Many Republican oppose Obama's moves toward better relations with Cuba, claiming they only bolster Cuba's communist leaders. Republicans also fear alienating Cuban Americans in Florida who have fled the island nation and are supporters of the Republican Party.

Obama charted a new U.S. path toward Cuba with the support of some Republicans, including freshman Senator Jeff Flake of Arizona.

Obama said in March his moves were already paying dividends, saying that since December the Cuban government had begun discussing ways to reorganize its economy.

McConnell has been a consistent critic of Obama on a range of foreign policy fronts, including Cuba and U.S. participation in multilateral nuclear talks with Iran.

"This president has been involved in ... talking to a lot of countries: talk, talk, talk. And Cuba is a good example. He thinks that simply by engaging with them we get a positive result," McConnell said, adding, "I don't see any indication that Cubans are going to change their behavior."

Human rights advocates have admonished Cuba for abuses, including arbitrary imprisonment of political opponents, and Cuba's tight control of its economy also has been a lightning rod for criticism.