"If Cuba is unwilling to make a better deal for the Cuban people, the Cuban/American people and the U.S. as a whole, I will terminate the deal," Trump tweeted.
Trump's threat came after the death of long-time Cuban dictator Fidel Castro, whose passing on Saturday he marked with another tweet. "Fidel Castro is dead!" the president-elect wrote, before issuing a statement condemning the Cuban leader.
Trump appears to be aiming to use the coming political transition in Cuba -- likely to be smoothed by the presence of Castro's brother Raul -- as a possible opportunity to renegotiate the terms of the rapprochement between the US and Cuba.
Speaking later Monday at the White House, spokesman Josh Earnest said the death of Castro is unlikely to have any impact on US effort to normalize relations between the two countries.
Earnest defended the policies of the Obama administration, but also said of Castro "there certainly is no whitewashing the kinds of activities that he ordered."
The spokesman said the President's statement Saturday on Castro's death -- which didn't criticize the Cuban leader -- "speaks for itself" and that Obama is focused on looking to the "future" with the goal of expanded the United States and Cuba's interests.
During his presidential campaign, Trump was an uneven critic of the détente with Cuba, alternately supporting the effort while criticizing the terms of the diplomatic negotiations.
In an interview with the Daily Caller in September, Trump had said the move was "fine." "50 years is enough," he said. "I think it's fine. I think it's fine, but we should have made a better deal. The concept of opening with Cuba is fine."
But a Miami rally in October, he took a more aggressive tone, saying he would reverse the deal unless Cuba met certain demands such as the "religious and political freedom for the Cuban people, and the freeing of political prisoners," without going into specifics. He called the Obama administration's negotiations "a very weak agreement."