Although the policy changes announced were limited, Trump tightened rules for Americans traveling to Cuba, banned ties with a military-run tourism firm and reaffirmed the existing U.S. trade embargo.
The government has though repeated its desire to engage in "respectful dialogue" with Washington.
Diplomatic relations, restored only two years ago, will remain intact, but Trump says some penalties will stay in place until a long list of prerequisites is met.
Trump's new policy will eliminate such self-certified visits by individuals while still allowing them to be done as group tours, and also retaining some individual travel under other authorized categories such as religious, artistic and journalistic activities, officials said. The president announced changes to Obama-era Cuba policy, and challenged the Castro government to negotiate a better deal.
The lengthy statement went on to strike a conciliatory tone, saying Cuba wants to continue negotiations with the USA on a variety of subjects.
However, Marriott International 's planned operations in Cuba may depend on the Trump administration's regulations, the hotel company said in a statement. Your clients can expect to enjoy the immersive, unforgettable experience they've been looking forward to as we visit Havana, Cuba on their upcoming sailing onboard Empress of the Seas. This will essentially shield USA airlines and cruise-ship companies now serving the island.
Worldwide human rights groups say, however, that renewed US efforts to isolate the island could worsen the situation by empowering Cuban hard-liners. "They will not achieve their goal of debilitating the Revolution or submitting the Cuban people, whose resistance to the aggressions of any kind and origin has been proven throughout six decades".
Moscow maintains close ties with Havana, and in March signed a deal to renew oil shipments to the Caribbean island for the first time in more than a decade.
And the USA government will police other trips to ensure travellers are pursuing a "full-time schedule of educational exchange activities". Under the expected changes, the US will ban American financial transactions with the dozens of enterprises run by the military-linked corporation GAESA, which operates dozens of hotels, tour buses, restaurants and other facilities.
"Last year I promised to be a voice against repression in our region", Trump said, "and a voice for the freedom of the Cuban people".
Central to US President Donald Trump's plans to peel back his predecessor's detente with Cuba is the idea that there is "good" and "bad" US travel.
The Cuban media called Trump's new foreign policy on Cuba "regrettable" and "archaic".
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Trump, in his speech at the Manuel Artime Theater near downtown Miami, announced that he was reversing those policies.
Yet it also exposed the shortcomings in Obama's approach. "We will enforce the embargo", Trump told a crowd in Miami. He is a dissident and an activist who lives in Cuba - and who traveled to Miami just to be here for Trump's speech, he says in Spanish.
"The Cuban people were so excited when President Obama came", Caridad Gonzalez, who runs a bed-and-breakfast, said.
"Deceiving the United States administration and appeasing militant outfits like Haqqani network, Taliban Quetta Shura and Al Qaeda operatives is a policy towed by ISI", the memorandum said. Cuban-Americans can send their funds to Florida.
"We will respect Cuban sovereignty", he said, "but we will never turn our backs on the Cuban people".
American travel to Cuba has been a political battleground since the early 1990s, when the collapse of the Soviet Union left the island's communist government starved for hard currency. His aides contend that Obama's easing of USA restrictions amounted to "appeasement" and has done nothing to advance political freedoms in Cuba, while benefiting the Cuban government financially. It was a policy shift by the United States government towards Cuba.
Cuba functioned as a virtual US colony for much of the 20th century, and even reform-minded Cubans are highly sensitive to perceived USA infringements on national sovereignty.
"I do believe that end is in the very near future", he said.
Negotiations on such issues as human rights and property expropriation by the Cuban government are underway.
Cuban state TV said: "The government of Cuba denounces the new measures toughening the embargo that are destined to fail". It was a win-win for the former president: Like Richard Nixon opened China, Obama opened Cuba.
Obama announced in December 2014 that he and Castro were restoring ties.