MIAMI (Reuters) - President Donald Trump on Friday ordered tighter restrictions on Americans traveling to Cuba and a clampdown on U.S. business dealings with the Caribbean island’s military, saying he was canceling former President Barack Obama's "terrible and misguided deal" with Havana.

Laying out his new Cuba policy in a speech in Miami, Trump signed a presidential directive rolling back parts of Obama’s historic opening to the Communist-ruled country after a 2014 diplomatic breakthrough between the two former Cold War foes.

But Trump left in place many of Obama’s changes, including the reopened U.S. embassy in Havana, even as he sought to show he was making good on a campaign promise to take a tougher line against Cuba, especially over its human rights record.

"We will not be silent in the face of communist oppression any longer," Trump told a cheering crowd in Miami’s Cuban-American enclave of Little Havana, including Republican Senator Marco Rubio of Florida, who helped forge the new restrictions on Cuba.

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"Effective immediately, I am canceling the last administration's completely one-sided deal with Cuba," Trump declared as he made a full-throated assault on the government of Cuban President Raul Castro.

Cuba later denounced the move as a setback in U.S.-Cuban relations, saying Trump had been badly advised and was resorting to "coercive methods of the past" that were doomed to fail. The government remained willing to engage in "respectful dialogue," it said in a statement.

Trump’s revised approach calls for stricter enforcement of a longtime ban on Americans going to Cuba as tourists, and seeks to prevent U.S. dollars from being used to fund what the Trump administration sees as a repressive military-dominated government. (tmsnrt.rs/2rBfMTI)

But, facing pressure from U.S. businesses and even some fellow Republicans to avoid turning back the clock completely in relations with Cuba, the president chose to leave intact some of his Democratic predecessor's steps toward normalization.

The new policy bans most U.S. business transactions with the Armed Forces Business Enterprises Group, a Cuban conglomerate involved in all sectors of the economy. But it makes some exceptions, including for air and sea travel, according to U.S. officials. This will essentially shield U.S. airlines and cruise lines serving the island.

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"We do not want U.S. dollars to prop up a military monopoly that exploits and abuses the citizens of Cuba," Trump said, pledging that U.S. sanctions would not be lifted until Cuba frees political prisoners and holds free elections.

While the changes are far-reaching, they appear to be less sweeping than many U.S. pro-engagement advocates had feared.

Trump based his partial reversal of Obama’s Cuba measures largely on human rights grounds.

His critics, however, have questioned why his administration is now singling out Cuba for human rights abuses but downplaying the issue in other parts of the world, including Saudi Arabia, a close U.S. ally Trump visited last month where political parties and protests are banned.

SOME OBAMA POLICIES LEFT IN PLACE

Trump, however, stopped short of breaking diplomatic relations restored in 2015 after more than five decades of hostilities. He also will not cut off recently resumed direct U.S.-Cuba commercial flights or cruise-ship travel, though his more restrictive policy seems certain to dampen new economic ties overall.

The administration, according to one White House official, has no intention of “disrupting” existing business ventures such as one struck under Obama by Starwood Hotels Inc, which is owned by Marriott International Inc, to manage a historic Havana hotel.

Nor does Trump plan to reinstate limits that Obama lifted on the amount of the island’s coveted rum and cigars that Americans can bring home for personal use.

Still, it will be the latest attempt by Trump to overturn parts of Obama's presidential legacy. He has already pulled the United States out of a major international climate treaty and is trying to scrap his predecessor's landmark healthcare program.

When Obama announced the detente in 2014, he said that decades of U.S. efforts to achieve change in Cuba by isolating the island had failed and it was time to try a new approach.

Critics of the rapprochement said Obama was giving too much away without extracting concessions from the Cuban government. Castro's government has clearly stated it does not intend to change its one-party political system.

Trump aides say Obama’s efforts amounted to "appeasement" and have done nothing to advance political freedoms in Cuba, while benefiting the Cuban government financially.

"It's hard to think of a policy that makes less sense than the prior administration's terrible and misguided deal with the Castro regime," Trump said in Miami.

International human rights groups say, however, that renewed U.S. efforts to isolate the island could worsen the situation by empowering Cuban hard-liners.

The Cuban government, which has made clear it will not be pressured into reforms, had no immediate comment.

But ordinary Cubans said they were crestfallen to be returning to an era of frostier relations with the United States with potential economic fallout for them.

"It's like we are returning to the Cold War," said Cuban designer Idania del Rio, who joined a group of friends in a hotel in Old Havana to watch the speech in English on CNN.

Trump announced his new approach at the Manuel Artime Theater in the heart of the United States' largest Cuban-American and Cuban exile community, whose support aides believe helped him win Florida in the election.

The venue is named after a leader of the failed U.S.-backed Bay of Pigs invasion of Cuba in 1961 against Fidel Castro’s revolutionary government.

“I have trust in Trump to do the right thing when it comes to Cuba,” said Jorge Saurez, 66, a retired physician in Little Havana.

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Trump’s vow to keep the broader decades-old U.S. economic embargo on Cuba firmly in place drew criticism from some U.S. farmers, especially growers of corn, soybeans and rice. Obama’s détente has already lifted exports and raised hopes for more gains, which they said were now in doubt.

Mexico’s foreign ministry urged the United States and Cuba to resolve their differences "via dialogue."

But Venezuelan President Nicolas Maduro, whose leftist government is Cuba's main regional ally, slammed Trump's tightening of restrictions as an "offence" against Latin America.

"His speech was aggressive and threatening, ... revealing his contempt and ignorance," President Nicolas Maduro said in a speech. "We reject Donald Trump's declarations against our brother Cuba. It is an offence against Latin America."

The biggest change in travel policy will be that Americans making educational people-to-people trips, one of the most popular authorized categories, can no longer go to the island on their own but only on group tours. Trump's aides said the aim was to close off a path for Americans seeking beach vacations in a country where U.S. tourism is still officially banned.

U.S. Senator Jeff Flake, one of the Republican Party's most vocal advocates for easing rules on U.S. dealings with Cuba, called for a vote on legislation lifting restrictions on American travel there. But the Republican leadership in Congress has long blocked such a move, and it appears unlikely to budge.

Under Trump’s order, the Treasury and Commerce departments will be given 30 days to begin writing new regulations, which will not take effect until they are complete.

In contentious deliberations leading up to the new policy, some aides argued that Trump, a former real estate magnate who won the presidency vowing to unleash U.S. business, would have a hard time defending any moves that close off the Cuban market.

But other advisers have contended that it is important to make good on a campaign promise to Cuban-Americans.

(Additional reporting by Matt Spetalnick, Lesley Wroughton and Patricia Zengerle in Washington, Sarah Marsh and Marc Frank in Havana, Bernie Woodall in Miami; writing by Matt Spetalnick; Editing by Jeffrey Benkoe, Yara Bayoumy, Jonathan Oatis and Lisa Shumaker)