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 66-year-old, of Ballybinaby, Hackballscross, County Louth, faces nine tax charges at the Republic of Ireland's Special Criminal Court.
Prosecutors claim he had significant dealings in cattle and land and received farming grants but failed to submit tax returns for nine years.
Mr Murphy denies the offences.
His defence lawyers claim that their client's brother, Patrick Murphy, managed his cattle herd and farming activities.
The prosecution at the three-judge, non-jury court was brought after an investigation by the Irish Criminal Assets Bureau (CAB).
One of the judges indicated that the verdict may be delivered next Thursday, 17 December, but added it is "by no means certain".
Mr Murphy was remanded on continuing bail until 17 December.

Reserve Bank of India governor Raghuram Rajan hinted that using cheap money to tackle economic problems - rather than painful reform - had to stop.
And he warned said that more intervention by central banks now risked doing "more harm than good".
Mr Rajan accurately predicted the global financial crisis in 2008.
In an exclusive BBC interview in Mumbai he said:  "I have been a little concerned about the immense burden for action that is falling on central banks and I think it is quite legitimate for central banks to say at some point  we can't carry the burden ourselves in fact we may not have the tools to do everything that is asked of us."
"Don't keep asking us to do more because at some point we get into territory where the consequences may be more bad than good if we actually act."
Mr Rajan acknowledged that his situation was not typical in the current climate, because unlike most global economies, India still has high inflation - running at close to 6%. Interest rates are also high - at  7.25% despite having been cut three times this year to try and stimulate growth.
"In my country I'm faced with traditional central bank problems like inflation so we still have a handle to work with those," Mr Rajan said.
He added: "But in some other countries you are faced with problems which are maybe way beyond what the central bank is capable of addressing such as demographic change, deep changes in productivity - and those are probably best dealt with other tools.
"But if the other tools aren't being used or there's a sense they'll take too long to work and you're working with the central bank only as the primary engine you may end up in situations that actually create more harm than good.
"Once interest rates are at zero it's hard to crank up new tools. Central banks have tried, they've tried very hard - negative interest rates,  low for long, quantitative easing, we've done a whole bunch of things like that.  The question is - at what point do you, through additional measures, do more harm than good?"
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.
[NEXT_CONCEPT]
The trial of the prominent republican Thomas "Slab" Murphy for alleged tax evasion has heard the court may deliver judgement on the case next week.
[NEXT_CONCEPT]
Central banks are under too much pressure to fix struggling economies, according to the man in charge of India's monetary policy.