Cuban Foreign Ministry issued a statement late yesterday calling the designation absurd.
It accused Washington of trying to justify the 52-year-old economic embargo against the island.
The US State Department's global terrorism report for 2013 notes that Havana is hosting peace talks between the Colombian government and that nation's biggest guerrilla army.
It says there is no information that the Cuban government is aiding any terrorist groups.
But it also mentions the presence of US fugitives in Cuba. The Cuban Foreign Ministry statement countered that none are terrorists, and those who committed crimes were punished on the island.