However, it says it will still co-operate with its larger neighbour.
Speaking earlier in Miami, Florida, Mr Trump said he was reimposing certain travel and trade restrictions eased by the Obama administration, condemning a "completely one-sided deal".
But he is not reversing key diplomatic and commercial ties.
"The government of Cuba denounces the new measures toughening the embargo," Cuban state TV said.
But it also reiterated "its willingness to continue the respectful dialogue and cooperation".
Barack Obama attempted to thaw relations by loosening trade and tourism bans.
President Trump says his new policy will tighten rules on travel and on sending funds to Cuba.
Announcing the changes on Friday, he cited human rights concerns, saying doing a deal with the "brutal" Castro government was "terrible" and "misguided".
Later that night, Cuban state news was also talking tough.
"Any strategy aimed at changing the political, economic and social system in Cuba - whether by pressure or imposition or through more subtle means - is destined to fail," it said.
However, President Trump is not rowing back on all parts of Obama's deal.
He will not close the US embassy in Havana, commercial flights from the US will continue, and Americans will still be able to return home with Cuban goods.
"The embargo should continue. Why give credit to a country where the people donÂ´t see a penny? They are still starving and there is no freedom whatsoever. Why should we keep feeding the people who are on top when they repress their own people." Jose Nadal
"I  am 100% Republican. I agree 150% with everything Trump says and does. They should impose more sanctions against Cuba. When Obama made the agreement and restored relations with the Cuban government, he gave them everything they asked for. We received nothing from the Cuban government. This is why Trump wants to strengthen the sanctions." Cathy Henderson
"I am against the embargo. The Cuban tyranny uses the embargo as a pretext to justify that it has failed. Everything bad that happens in Cuba, they blame the embargo." Santiago Portal
Courtesy of BBC Mundo
1959: Cuban revolutionary Fidel Castro leads a guerrilla army into Havana overthrowing the Batista regime.
1960: In response to Castro's communist reforms, US breaks off diplomatic relations with Cuba and imposes a trade embargo.
1962: Castro agrees to allow the Soviet Union to deploy nuclear missiles on the island bringing the US and the USSR to the brink of nuclear war.
April 2009: President Barack Obama lifts restrictions on family travel and the sending of remittances to Cuba.
July 2015: The US and Cuba reopen embassies in each other's capitals and restore full diplomatic ties.
March 2016: President Obama makes a three-day visit to Cuba and holds talks with President Raul Castro. He expresses hope the embargo will be ended, but it can only be lifted by the US Congress which is controlled by Republicans who oppose the move.
Aug 2016: US commercial flight arrives in Cuba for the first time in more than half a century.
Cuba's government has denounced US President Donald Trump's decision to roll back on policy changes towards the island nation.