President Donald Trump arrives to speak about Cuba policy, June 16, 2017, in Miami.
President Donald Trump arrives to speak about Cuba policy, June 16, 2017, in Miami.

WHITE HOUSE - Saying he was "canceling the last administration's completely one-sided deal with Cuba," President Donald Trump on Friday began undoing some parts of his predecessor's historic opening to the island nation.

The new measures included tighter restrictions on tourism travel and a prohibition of financial dealings with entities tied to Cuban military and intelligence services. Cuba's military conglomerate GAESA is estimated to control more than half the country's economy.

Watch: Trump Recasts Cuba Policy, Slams Castro

In a speech at Miami's Little Havana district, flanked by Vice President Mike Pence, Florida Republican Senator Marco Rubio and other leading politicians of Cuban descent, Trump said he took steps toward fulfilling a campaign promise that helped him win last November's election in the battleground state of Florida, where the Cuban-American vote was instrumental in pushing him over the top.

"America has rejected the Cuban people's oppressors,'' he told a cheering crowd at the packed, sweltering Manuel Artime Theater, named after a leader of the ill-fated Bay of Pigs invasion. "I do believe that the end is in the very near future."

WATCH: Trump on new Cuba policy

"We will enforce the ban on tourism. We will enforce the embargo. We will take concrete steps to ensure that investments flow directly to the people so they can open private businesses and begin to build their country's great, great future," Trump said.

The Cuban government said Friday in a statement that it “reiterates its willingness to continue with respectful dialogue and cooperation on issues of mutual interest” with the U.S. The statement said Cuba and the U.S. have demonstrated in the last two years that “they can cooperate and live together civilly, respecting differences and promoting that which benefits both countries and peoples.”

Cuba warned, however, that the U.S. “should not expect Cuba to make concessions on its sovereignty and independence, nor will it accept any type of such conditions.”

Some policies remain

White House officials, however, said many of the changes that occurred under former President Barack Obama would remain in place.

According to senior administration officials, Americans will still be able to travel to Cuba under approved categories, but there will be stricter enforcement to ensure travelers fit those categories.

WATCH: Trump message to Cuban leadership

Americans will be permitted to bring back souvenir items such as rum and cigars. Commercial flights between the United States and Cuba will continue, and diplomatic relations will not be affected, though Trump will not name an ambassador to Havana.

Obama had halted the so-called "wet foot/dry foot" policy that had allowed Cubans who arrived on U.S. shores to apply for work permits that could eventually lead to citizenship — a move that will not be touched by Trump's rollback.

Policy pushback

Obama initiated the move to normalize relations with Cuba and ease a long-standing trade embargo in 2014. He argued it was time to adopt a policy of engagement with the Cuban people because the decades-old embargo of the communist nation had failed to bring change to the island.

In 2016, he traveled to Havana to meet President Raul Castro, but not his brother Fidel, who led the overthrow of Cuban dictator Fulgencio Batista more than half a century earlier.

FILE - People put their luggage in a private taxi
FILE - People put their luggage in a private taxi as they arrive from the U.S. to the Jose Marti International Airport in Havana, Cuba, Sept. 1, 2014.

Several Obama-era officials derided the partial Trump rollback, arguing that more restrictive policies send the wrong signal to America's friends and adversaries alike.

"I think history shows that the surest path to progress is through engagement. We've seen it in Vietnam, across Europe in World War II, in Iran and Burma, where our people-to-people diplomacy paved the way for change on the ground," said Brett Bruen, who served as Obama's director of global engagement.

"Raul Castro and those in power in Havana are not going to loosen their grip on power because we tighten our grip on the island," Bruen told VOA. "It's only going to cut off paths to opportunity and strengthen the arguments they're making that the U.S. is not a partner for the Cuban people."

Private jeweler and electronics technician Gabriel
Private jeweler and electronics technician Gabriel La O repairs a mobile phone inside a government store where he rents work space in Havana, May 24, 2016. Cuba says it will legalize small and medium-sized private businesses.

Support on human rights

While business interests have cautioned against any move that would weaken growing U.S.-Cuba trade ties, Republicans' reactions have been strongly supportive of Trump's moves. House Foreign Affairs Committee Chairman Ed Royce of California, in a statement sent to VOA, said the United States must stand with the Cuban people in their fight for basic freedoms.

"President Obama's new course with the Castros led to more brutality, more repression, and more political arrests in Cuba," Royce wrote. "The administration is right to sideline the Cuban military and make human rights and internet access top priorities."

Some Cuban-Americans praised the symbolism of Trump's rollback, if not the substance.

"The Castro regime has done nothing about human rights," said Mike Gonzalez, who as a youth in Cuba listened surreptitiously with his family to VOA shortwave radio broadcasts.

U.S. President Barack Obama attends a meeting with
FILE - Then-U.S. President Barack Obama attends a meeting with Cuban dissidents at the U.S. Embassy in Havana, Cuba, March 22, 2016. On the wall behind Obama is a painting, "My New Friend," donated to the embassy by Michel Mirabal, a Cuban artist.

Gonzalez, now a fellow at the conservative Heritage Foundation in Washington, likened Trump's Little Havana appearance to President Ronald Reagan's famous Cold War speeches.

"The Brandenburg Gate speech by Reagan, where he said, 'Mr. [Mikhail] Gorbachev, tear down this wall,' in 1987, is being remembered this week because the 30th anniversary just passed, and many people are saying,'Yeah, I heard that in East Berlin, and that was powerful,' " Gonzalez said. "We don't have to be the world's policeman but we have to make clear to all tyrants that we are on the side of the people they oppress."

Administration officials said the changes would not go into effect immediately. The Treasury and Commerce departments will have 30 days to draft new regulations, and it will take an unspecified amount of time before implementation can take place. "It will take as long as it takes," said one official.