President Raul Castro said "attempts to destroy the revolution" would fail.
Mr Trump has tightened restrictions on US travel to and business with the communist island.
But the US embassy in Havana, re-opened by former President Barack Obama, is still operating.
Mr Castro was speaking in front of Cuba's national assembly. It was his first public comment on the policy changes Mr Trump announced a month ago.
State-run Cuban media quoted Mr Castro as saying that Mr Trump was using "old and hostile rhetoric" and had returned to "confrontation that roundly failed over 55 years".
He said: "We reject the manipulation of the topic of human rights against Cuba, which can be proud of much in this area and does not need to receive lessons from the United States nor anyone."
Mr Trump anchored his policy rollback in human rights concerns raised by political opponents of Cuba's communist government, many of whom have fled to Miami where Mr Trump announced the changes on 16 June.
Mr Castro continued: "Cuba and the United States can cooperate and live side by side, respecting their differences. But no one should expect that for this, one should have to make concessions inherent to one's sovereignty and independence."
Mr Castro will step down as president in seven months, but will remain the head of the country's Communist Party.
The president of Cuba has spoken publicly for the first time against US President Donald Trump's rollback of a thaw between the two countries a month ago.