However, Cuba said it would still cooperate 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".