Trump's words came in a tribute on Cuban Independence Day, which marks victory against the Spanish colonial authorities 115 years ago, calling for economic freedoms and respect for human rights in Cuba.
"Cruel despotism cannot extinguish the flame of freedom in the hearts of Cubans, and... Unjust persecution cannot tamper Cubans' dreams for their children to live free from oppression," he said in a statement.
Cuban television broadcast its response late in the evening, describing Trump as "the ill-advised US president" and his statement as "controversial and ridiculous."
The broadcast did not say whether the Cuban statement constituted an official response, nor did it directly address Trump's criticisms.
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One-party communist Cuba has been ruled by President Raul Castro for 12 years since he took over from his ailing brother Fidel, the revolutionary leader who died in November having defied the United States during a half-century of iron-fisted rule.
Former US president Barack Obama presided over an opening toward Cuba that saw full diplomatic ties restored after decades, but Trump has threatened to roll back the historic rapprochement.
Castro, 85, has said that he will step aside in February 2018. It is not clear who will take his place next year.
Cuba officially became an independent nation on May 20, 1902 after fighting a war of independence, backed by the United States, against Spain from 1895-98.
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