Donald Trump has threatened to "terminate" the diplomatic relationship with Cuba negotiated by President Barack Obama.
In a tweet, the President-elect said: "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."
In another development, the President-elect is to meet retired general David Petraeus later, as he reportedly considers him for the role of secretary of state.
Mr Trump will also meet former Republican presidential nominee Mitt Romney, another rumoured choice for secretary of state, on Tuesday.
The President-elect's tweet about Cuba comes just a day after senior advisers to Mr Trump pledged to strike a "better deal" with the Caribbean island following former leader Fidel Castro's death last week at the age of 90.
Mr Trump's team has said the outgoing administration made too many concessions to Cuba, such as easing the long-standing economic embargo, without getting enough in return on topics including human rights and democracy.
Speaking on Fox News Sunday, the President-elect's chief of staff, Reince Priebus, said: "We've got to have a better deal."
In March, Barack Obama became the first US president to visit Cuba in 88 years.
The two countries announced they would re-open diplomatic relations in December 2014, ending an estrangement that began when the Cuban revolution ousted a pro-American government in 1959.
Mr Obama was greeted initially by foreign minister Bruno Rodriguez - not the president, Raul Castro.
Mr Trump tweeted at the time: "Wow, President Obama just landed in Cuba, a big deal, and Raul Castro wasn't even there to greet him. He greeted Pope and others. No respect."
Despite the thawing of relations, some tensions remained.
During Mr Obama's visit, Mr Castro looked annoyed when asked about political prisoners during a news conference.
Meanwhile, Mr Trump has claimed he would have won the US popular vote were it not for the "millions of people who voted illegally".