His aides contend that Obama's easing of US restrictions amounted to "appeasement" and has done nothing to advance political freedoms in Cuba, while benefiting the Cuban government financially.
Still, Cuba said it is willing to continue "respectful dialogue" with the U.S. on topics of mutual interest.
In December 2014, former USA president Barack Obama announced that the United States would normalize relations with Cuba after more than 50 years of non-engagement and hostilities.
However, Trump will stop short of closing embassies or breaking diplomatic relations restored in 2015 after more than five decades of hostility and will not cut off recently resumed direct U.S. -Cuba commercial flights - though his more restrictive policy seems certain to dampen new economic ties.
"The Cuban government denounces the new measures hardening the blockade that are destined to fail ... and that will not achieve their aim of weakening the revolution", Havana said.
Donald Trump in Miami announcing his new policy on Cuba.
"It's hard to think of a policy that makes less sense than the prior administration's bad and misguided deal with the Castro regime", Trump said in Miami.
Earlier, Trump signed an executive order to enact numerous immigration policies, including the construction of a wall on the US-Mexico border.
The statement added that Havana will continue to work with the U.S.in the matters of common interests, but will not make concessions inherent to its sovereignty and independence.
Civil Rights Commission Launches Investigation Into Ed. Dept., Other Agencies
DeVos' press secretary, Elizabeth Hill said the rules are meant to speed up the resolution of complaints. The Department of Education did not return a request for comment by NBC News .
It was Trump's most public statement yet calling on a foreign government to improve its human rights record, one that came with specific promises to cut off U.S. cash flows that could support the communist regime in Havana.
Under the new regulations, Americans will no longer be able to take private trips to the island, and US companies and citizens will be barred from doing business with entities controlled by Cuban government agencies, including its military and security services.
The Cuban government maintained that the new policies would not work, comparing it to the economic embargo that never ushered the Castro regime out of power as the USA had hoped. Harmful changes like these are a prime example of why Congress must act to codify the law and allow open trade and travel with Cuba and the Cuban people.
Its statement takes a swipe at the United States under Trump by noting issues that negatively affect Americans, including racial discrimination and gun violence, and controversial policies on immigration, a border wall and abandoning the Paris Agreement on climate change. Previously, Cubans who reached USA shores earned automatic visas.
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.
The past two years has shown that the two countries, as Cuban President Raul Castro has repeated, can cooperate and live together in a civilized manner, respecting differences and fostering everything that can benefit both nations and people, the statement points out. But it makes some exceptions, including for air and sea travel, according to U.S. officials. 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.
"I do believe that end is in the very near future", he said.
Obama announced in December 2014 that he and Castro were restoring ties.
Among the few Cubans on the island who praised Trump was Berta Soler, a leader of the dissident group Ladies in White who said she was prevented by the government from flying to Miami to attend the speech in person.