(CNN) Cuba's longtime revolutionary leader Fidel Castro died Friday, bringing the possibility of further change to an island whose relations with the United States had only recently begun to thaw.

But Castro's death comes ahead of real change in the White House, with President-elect Donald Trump threatening to undo efforts by President Barack Obama to bring the US and Cuba closer together.

Trump has frequently criticized the deal Obama struck to reopen diplomatic relations with Cuba and entertained reversing moves to re-establish some trade with Cuba.

In an October interview with a local CBS station in Miami, Trump criticized the Obama administration's effort to normalize relations with Cuba as a "very weak agreement," though he said some sort of a deal is "fine."

Trump also told CBS4 interviewer Jim Defede that he would do "whatever you have to do to get a strong agreement," even if that meant breaking off the recently-resumed diplomatic relations.

At a rally in Miami earlier in September, Trump had also blasted the Cuba policy changes, an apparent shift from past statements in which he supported the reopening of diplomatic relations after more than 50 years.

In March, the businessman expressed interest in opening a hotel in Cuba, telling CNN it was "OK to bring Cuba back into the fold."

Delicate moment

Speaking after Castro's death, CNN analyst Peter Kornbluh said it was a "very delicate moment" in US-Cuban relations.

"The Cubans -- like many other countries around the world -- really don't know what to expect and have great fears about what to expect from a Donald Trump administration.

"With Fidel's passing, the news cycle on this -- the statements that are being made, the images from Miami, whatever Trump actually comes out and says -- really will set the tone for whether this reconciliation and rapprochement between Washington and Havana continues in the post-Obama era," Kornbluh said.

"And we could easily go the route of having great tensions if the Cubans perceive a Trump administration trying to take advantage of what they believe to be instability in the wake of Fidel's passing -- or we could have a more rational approach and everybody understands that this doesn't really change the relationship between the United States and Cuba and certainly doesn't change the future of leadership for the foreseeable future in Cuba," he said.

CNN en Espanol correspondent Juan Carlos Lopez said it was "anyone's guess" as to what would happen under Trump.

"We still don't know who his secretary of state will be, we don't know what his policy towards Latin America will be."

Meantime Miami Herald reporter Glenn Garvin told CNN that if Trump pulled back on the changes brought in by Obama. "That will set US relations with Cuba back to where they were the past 50 years."

Clinton vs. Trump in Cuba

Sebastián Arcos, associate director of the Cuban Research Institute at Florida International University, told CNN in September that Cubans were looking forward to the future because of the improved relations between Havana and Washington.

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"They see (the changes) with optimism. For a simple reason: They've been told that the problems in Cuba are a result of the hostility of the United States," he said. "When the President says there's no longer any hostility, they are optimistic about the change."

Arcos said Cubans were leaning toward Democratic presidential candidate Hillary Clinton over Trump mostly because of Clinton's shared policies with Obama.

"The Cuban propaganda machine is promoting Hillary Clinton," he said. "Whatever they are telling Cubans about the election is filtered, but that's usually the message."

Clinton was the first major presidential candidate to advocate lifting the US embargo on Cuba.

In Miami last year, she called for the trade blockade to end: "The Cuba embargo needs to go, once and for all."

Freeing of prisoners

Cuba freed 53 political prisoners in January 2015 as part of its deal to reopen diplomatic relations with Washington.

The US restored full diplomatic relations with Cuba in July 2015 following more than 50 years of Cold War tensions. President Obama loosened a series of regulations at the time allowing more US companies to sell their products in Cuba although the US embargo on Cuba remains in place.

Obama argued that the reopening could lead to making Cuba more free society, but Trump argued that the Cuban regime needed to meet his demands to restore political freedoms and free political prisoners.

"But all of the concessions that Barack Obama has granted the Castro regime were done with executive order, which means the next president can reverse them. And that is what I will do unless the Castro regime meets our demands," Trump told Miami voters in September.

"Those demands will include religious and political freedom for the Cuban people and the freeing of political prisoners," he added.