"The government of Cuba denounces the new measures toughening the embargo" imposed since 1962, according to a statement read on state television yesterday.
But it also reiterated "its willingness to continue the respectful dialogue and cooperation".
Members of Congress who favor closer U.S. -Cuba ties have urged Trump to maintain Obama's approach.
"Easing of restrictions on travel and trade does not help the Cuban people", he said at an event in Miami on Friday.
It's a policy change President Trump insists will correct what he called a "terrible and misguided deal" by his predecessor.
But Trump has, in the past, apparently done business in Cuba - in violation of the embargo the USA had in place against the country. "We will not lift sanctions on the Cuban regime until all political prisoners are free".
In its response, Cuba accused Trump of using "coercive methods from the past".
'We recall that Cuba is a State party to 44 global human rights instruments, while the United States comply with only 18, therefore we have much to show, comment and defend, ' the island's government upholds.
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Diplomatic relations are still open between the two countries. and no restrictions on any goods that the U.S can benefit from Cuba by forbidding trading with businesses run by Military or Intelligence services. At the very least, we should not restrict Americans' freedom to travel unless there is strong evidence that doing so really will have a substantial beneficial effect on human rights in Cuba. Most US business deals with the Armed Forces Business Enterprises Group are also likely to be banned.
While tourism to Cuba is banned by US law, the Obama administration had been allowing people to travel to Cuba as part of "people to people" educational trips for visitors, a popular classification that a White House official said was "ripe for abuse" by those looking for beach vacations.
Security agencies and senior officials in Cuba said they are willing to continue cooperation with the US side, despite that exchanges have declined sharply since Trump took office in January.
Obama traveled to Havana last March to solidify a detente between the USA and Cuba that his administration negotiated in 2014. He vowed to seek a "much better deal for the Cuban people and for the USA".
But the overwhelming majority of the Cuban economy is controlled by the government. "Return the fugitives from American justice".
But the changes would ultimately meet four objectives, according to the White House: Ensure compliance with US law, hold the Cuban government accountable for alleged human rights abuses, further the interests of the USA and the Cuban people, and "empower the Cuban people to develop greater economic and political liberty". "It's the people who'll suffer the consequences, not the Cuban state".
The Obama administration argued that decades of isolation had failed to produce changes in the Cuban regime and sought a diplomatic and economic opening between the nations.
But Trump was leaving many of Obama's changes, including the reopened USA embassy in Havana, in place even as he sought to show he was making good on a campaign promise to take a tougher line against Cuba.
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