President Trump on Friday announced the reversal of some of former President Barack Obama's policies towards Cuba, and told a cheering crowd in Miami that he was "canceling the last administration's completely one-sided deal with Cuba."

"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. The president then added, "You have to say, the Iran deal was pretty bad also. Let's not forget that beauty."

Trump promised during the campaign to roll back Obama's Cuba opening executive orders. But senior White House officials acknowledged that Trump isn't moving to repeal all of Obama's actions, and will instead restrict a narrow category of travel and restrict transactions that aide Cuba's military and intelligence agencies.

In his speech in Miami, however, Trump put pressure on the Cuban government to return fugitives from U.S. justice who have found safe harbor in Cuba. One of them is Joanne Chesimard, who was convicted of killing a New Jersey state trooper, and whom Trump mentioned by name in his speech.

Supporters of trade and travel restrictions against Cuba have argued for years that Cuba's harboring of fugitives is a chief reason not to reach out to the Castro regime. Trump spelled out the other major reason in his speech Friday: that certain transactions with Cuba only profit the Castro government, something he said the U.S. must avoid as it tries reaching out to the Cuban people.

"The profits from investment and tourism float directly to the military," Trump said. "The regime takes the money and owns the industry. The outcome of the last administration's executive action has been only more oppression and a move to crush the peaceful democratic movement."

Trump repeatedly characterized his actions as keeping his campaign promise to the Cuban-American community.

"Last year, I promised to be a voice against repression. In our region, remember, tremendous repression," Trump said. "And a voice for the freedom for the Cuban people. You heard that pledge, you exercised the right you have to vote. You went out and you voted. And here I am like I promised, like I promised."

"Now we hold the cards," Trump said. "We now hold the cards. The previous administration's easing of restrictions on travel and trade does not help the Cuban people. They only enrich the Cuban regime."

However, Trump's action keeps many of Obama's major moves in place. Licensing rules for authorized travel will not be tightened, and Americans returning from Cuba will be able to bring back as much Cuban rum and Cuban cigars as they can carry. Trump's move also doesn't demote the status of the new U.S. embassy in Cuba.

One key change, however, will be the elimination of "people-to-people" travel to Cuba on an individual basis. Obama allowed individuals to go to Cuba and assert on their own that their trip was educational in nature and thus compliant with U.S. law that prohibits tourism.

But the Trump administration thinks that arrangement is a recipe for fraud that makes it too easy for people to visit Cuba as tourists.

The rules will prohibit people from staying at hotels owned by the Cuban military, and the State Department will create a list of entities Americans should avoid.

Trump's new policy will also keep in place Obama's decision to end the "wet foot, dry foot" policy, which gave Cubans a path toward permanent residency if they arrived in the United States. Obama said at the time that the policy unfairly gave preference to one group of immigrants over others, and Trump said Friday that the change makes sense because it keeps Cubans from trying to make the dangerous journey to the U.S. over water.

Trump cited two Cuban-American Republican lawmakers who have pushed for a tougher stance against Cuba — Florida Sen. Marco Rubio and Florida Rep. Mario Diaz-Balart — who helped craft the policy and who were with with Trump on Friday.

"More than anything else, this change empowers the people of Cuba, not the government, not the regime, but the people," Rubio told the crowd before Trump's speech. "So that they can enjoy the freedom and the liberties with a very clear message: America is prepared to outstretch its hands and work with the people of Cuba., but we will not empower their oppressors."

Democrats are opposing the reversal. New York Democratic Rep. Eliot Engel, the ranking member of the House Committee on Foreign Affairs, called Trump's actions "a step backward in the rapprochement between our two countries."

"In particular, restricting the travel of American citizens will only serve to further isolate the Cuban people from the outside world," Engel said.

Ahead of the announcement, three Republican senators who support an opening with Cuba — Arizona Sen. Jeff Flake, Wyoming Sen. Mike Enzi and Arkansas Sen. John Boozman — urged the Trump administration to "weigh carefully any rollback of policies." In a letter, they said Obama's changes provided a "critical strategic advances that have already benefited everyday Cubans and provided direct benefits to Americans by enhancing U.S. national security and boosting the U.S. economy."

The business community is also criticizing the move. "Unfortunately, today's moves actually limit the possibility for positive change on the island and risk ceding growth opportunities to other countries that, frankly, may not share America's interest in a free and democratic Cuba that respects human rights," the U.S. Chamber of Commerce said in a statement.

José Ramón Cabañas, Cuba's ambassador to the United States, mocked the announcement, tweeting a photo of tourists in Cuba and saying: "Now it is official: these are the new enemies of US Foreign Policy. Watch out!!"