Trump has threatened to end the US thaw with Cuba unless Havana delivers a "better deal" for Washington and makes concessions on human rights and opening up its economy.
He also described the late Cuban leader Fidel Castro as a "brutal dictator" after the revolutionary icon died on November 25.
Nevertheless, Cuba "would hope the new government of the United States takes into account the results we have achieved" since diplomatic ties were re-established in 2015, and would be ready to continue improving them "on the basis of respect," said Josefina Vidal, head of US affairs at the Cuban foreign ministry.
Cuba reaffirmed its will "to continue making progress in improving relations and building ties of peaceful coexistence, beneficial to both sides," Vidal said.
However, this must happen "within respect for the existing differences, and without having to make any type of concession or abandoning the principles in which Cuba firmly believes in," she said.
The United States and Cuba re-established ties in July 2015 after a rupture of more than half a century.
Despite advances in relations between the former Cold War rivals -- which include a slew of bilateral agreements and more than 208,000 US citizens visiting Cuba this year -- Washington has not lifted the economic embargo imposed on the island in 1962.
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