"If Cuba is unwilling to make a better deal for the Cuban people, the Cuban/American people and the US as a whole, I will terminate deal," Trump said in a Twitter post.
Trump tweeted as Cubans prepare to commemorate Fidel Castro, the communist guerrilla leader who led a revolution in 1959 and ruled the Caribbean island for half a century. Castro died on Friday.
On Saturday, Trump said in a statement that his administration would "do all it can" once he takes office on Jan. 20 to boost freedom and prosperity for Cubans after Castro's death.
The statement sidestepped regarding whether Trump would follow through on a threat made late in his White House campaign to reverse Obama's diplomatic thaw with the island nation, leading some to view it as a softening from his campaign rhetoric toward the country.
Castro's death has led some Cubans to worry that Trump will shut down the US-Cuban trade and travel ties that have begun to emerge in the past two years since Obama's historic declaration.
Cuba has resisted what it sees as US attempts to influence and change its internal political system, but the government has stayed mostly quiet on Trump, waiting to see whether the president-elect translates his harsh rhetoric into real policy change.