The sharply worded Foreign Ministry statement came after US and Cuban delegations met in Washington to discuss bilateral relations, the first such high-level meeting between the Cold War foes since Trump took office in January, Reuters reported.
Their meeting took place on the same day Trump addressed the United Nations General Assembly in New York, calling Cuba "corrupt and destabilizing." He also said he would not lift the US trade embargo on Cuba until it made "fundamental reforms."
Cuba said it had voiced "strong protest" against his comments, as well against his new policy toward the Communist-run nation. The Republican president announced in June a partial rollback of the US-Cuban detente forged by his Democratic predecessor, Barack Obama.
"In the wake of the disrespectful, unacceptable and meddling statements made by President Donald Trump in his address to the UN General Assembly at a time when the US-Cuba Bilateral Commission was sitting in session, the Cuban delegation voiced a strong protest," the Foreign Ministry statement said.
US-Cuban relations have become especially strained since the State Department said last month its personnel in Havana had experienced physical symptoms from what it could only describe as "incidents."
The symptoms ranged from hearing loss to mild brain injury, a State Department official said last week, adding that the toll of victims had risen to 21 people linked to the US Embassy. Several Canadians were also affected.
Cuba has denied any involvement and the United States has not blamed it, although Secretary of State Rex Tillerson said on Sunday it could close its embassy in response.
"Cuba has never perpetrated or will ever perpetrate actions of this nature, and has never permitted or will ever permit any third-party use of its territory for this purpose," Cuba's Foreign Ministry said.
"The Cuban authorities have shown keen interest in both clarifying this matter."