On Saturday, Pompeo told the UN Security Council that Cuba had "directly made matters worse" in Venezuela.
"These interventionist threats, full of slander and arrogance, will get blown to pieces when they face the determination of people that have never given up on their independence and sovereignty," Diaz-Canel posted on Twitter late on Saturday.
Earlier in the day, Anayansi Rodriguez Camejo, the permanent representative of Cuba to the United Nations, accused Washington of using the Security Council as a platform for legitimization of its international campaign against the constitutional government of the country's president, Nicolas Maduro.
She also voiced belief that aggression by the United States and its allies was the main threat for peace and security in Latin America.
On Tuesday, the situation in Venezuela, which is going through a political crisis, escalated dramatically when the opposition-controlled National Assembly declared that Maduro had usurped power. Opposition leader Juan Guaido proclaimed himself interim president on the following day.
The United States along with some other states recognized Guaido as the interim president, after which Maduro accused Washington of organizing a coup in Venezuela. Maduro also decided to cut off diplomatic relations with the United States and asked US diplomats to leave the country within 72 hours.
Cuba, along with Russia, Mexico, and other countries, has expressed support for Maduro as legitimate Venezuelan president.