Donald Trump says he will end the thaw between the US and Cuba if the country does not offer a "better deal".
President Barack Obama has worked to improve relations with the communist government in Havana, culminating in his historic visit in March 2016.
The president-elect threatened in a tweet to put an end to the detente following the death of Fidel Castro.
But the White House bristled at Mr Trump's warning, saying the president was not concerned about the threat.
White House Press Secretary Josh Earnest told reporters that reversing the policy would be "a significant economic blow" to Cubans and was "not as easy as a stroke of a pen".
President-elect Trump tweeted he would "terminate" Mr Obama's policy on normalising relations with Cuba as thousands of Cubans queued to pay their respects to , who died on Friday.
They gathered in Havana's Revolution Square as part of farewell commemorations which will last until Tuesday night, when foreign leaders are due to arrive in Cuba to pay their respects.
A cortege will then transport his ashes east across the island to Santiago de Cuba, reversing the route Castro took during the Cuban revolution.
They will be laid to rest on Sunday in the city's Santa Ifigenia cemetery.
In his tweet, Mr Trump said that 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".
Mr Trump, who takes office in January, said during the election campaign that he would reverse President Barack Obama's rapprochement with Cuba.
Under Mr Obama, diplomatic ties were restored in 2015 after being severed in 1961. Some trade restrictions have been eased and the White House has been lobbying the US Congress to terminate an economic embargo that has been in place for decades.
Mr Trump's team has accused the Obama administration of giving too much away to Cuba without receiving enough in return.
His communications director, Jason Miller, said Mr Trump was seeking "freedom in Cuba for the Cubans and a good deal for Americans where we aren't played for fools".
But the White House said that better ties with Cuba served US interests and that reversing the changes would deal "a significant economic blow" to the people of Cuba.
"After five decades of not seeing results, the president believed it was time to try something different," said White House spokesman Josh Earnest.
In a separate development the first scheduled commercial flight from the US to Havana in more than 50 years has departed from Miami.
The American Airlines (AA) flight on Monday morning was the first of a new service to the Cuban capital which will fly from Florida four times a day.
"It's a monumental day of great historic relevance with Miami being the epicentre of the Cuban-American community and American's hub for the region," AA Vice President Ralph Lopez was quoted by The Miami Herald as saying.
Several airlines began routes to other parts of Cuba earlier this year, with many more flights and destinations in the offing.