The President said it was hard to think of a policy "that makes less sense than the prior administration's bad and misguided deal" with the "brutal" Castro government.
A pro President Donald Trump supporter chants slogans, Friday, June 1, 2017, in Miami.
Saying that the aim was to fix what Trump has called a "bad deal" struck by Obama, U.S. officials said the new administration would leave the door open to improved relations if Cuba undertakes democratic reforms such as allowing free elections and releasing political prisoners.
The new policy aims to starve military-linked businesses of cash by banning any US payments to them.
By signing Friday afternoon a presidential national security directive, Trump imposes additional hurdles to the very restricted business opportunities American companies had to trade and invest in Cuba, the statement underlines. Still, Cuba said it is willing to continue "respectful dialogue" with on topics of mutual interest.
"More travel, more communications access, and more dialogue with Cuba are the way forward for human rights in Cuba", Amnesty International wrote in a blog post, adding that Obama's trip to Cuba last year opened the door to "scrutiny and transparency" of human rights on the island for the first time in almost 10 years. Diplomatic relations, restored only two years ago, will remain intact. But Trump vowed that trade and other penalties would stay in place until a long list of prerequisites is met. The self-directed, individual travel permitted by the Obama administration will be prohibited.
Mr. Trump will reinstate travel and commercial restrictions eased by Mr. Obama previous year, during that administration's attempts to obtain additional concessions from the Cuban government.
"I am concerned it will affect the private sector quite a bit and much more than the Cuban government", he said.
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Sanders later condemned the shooting and said that he had been made aware that Hodgkinson had volunteered for his campaign. The FBI is also investigating the incident, saying they're not sure if the shooting was an assassination attempt.
Moran said in a statement that "putting America first means exporting what we produce to countries across the globe". Other dissidents agree repression has worsened but say rolling back the detente, which will hurt ordinary Cubans, is not the solution.
Granma, the official organ of Cuba's Communist Party, described Trump's declarations in real-time blog coverage Friday as "a return to imperialist rhetoric and unilateral demands".
The Cuban government has given Trump's speech extensive coverage on official media.
"Our embassy remains open in the hope that our countries can forge a much stronger and better path", he said.
But, facing pressure from US business and some of his fellow Republicans to avoid turning back the clock completely in relations with communist-ruled Cuba, he also will leave intact many of Obama's steps toward normalization. A former Cuban soldier who arrived in the U.S.by boat in 1959, he said that that Trump measures were the right ones to take.
The statement reiterates Cuba's commitment to "the necessary changes that we're making now as part of the updating of our socio-economic model", but says "they will continue being decided in a sovereign way by the Cuban people".
Hundreds of millions of USA dollars flowed into privately owned businesses in Cuba, The Associated Press reported, spurring the growth of a nascent middle-class that could thrive independent from the government. "All the (U.S. economic) embargo has brought upon Cuba is misery".
A landmark agreement to normalise relations between the former Cold War foes was made between former US President Barack Obama and Cuban leader Raul Castro in 2014.
Weissenstein reported from Havana and Lederman from Washington.