HAVANA, March 16 (Reuters) - U.S. President Donald Trump escalated his rhetoric against Cuba on Monday, saying he expected to have the "honor" of "taking Cuba in some form" and that "I can do anything I want" with the neighboring country.

The threatening statements come even as Cuba and the United States have opened talks aimed at improving their largely adverse relations, which have reached one of their most contentious moments in the 67 years since Fidel Castro overthrew what had been a close U.S. ally.

"I do believe I'll be ... having the honor of taking Cuba. That's a big honor. Taking Cuba in some form," Trump told reporters as the island faces an unprecedented economic crisis, exacerbated by an oil blockade the U.S. imposed after capturing former Venezuelan President Nicolas Maduro.

"I mean, whether I free it, take it. Think I can do anything I want with it. You want to know the truth," Trump told reporters at a signing event in the Oval Office.

After Trump spoke, the New York Times reported that removing Cuban President Miguel Diaz-Canel from office is a key U.S. objective in the bilateral talks. Citing four people familiar with the talks, the Times said the Americans have signaled to Cuban negotiators that Diaz-Canel must go but are leaving the next steps up to the Cubans.

Cuba has traditionally rejected any interference in its internal affairs and has considered any proposals on that front a deal-breaker for any agreement.

Diaz-Canel, 65, who succeeded the late Fidel Castro and his brother Raul Castro as president in 2018, said on Friday he expected talks with the United States to take place "under the principles of equality and respect for the political systems of both countries, sovereignty and self-determination."

But Trump, after removing Maduro from power and joining Israel in attacking Iran, has openly mused that Cuba would be "next." He stepped up pressure by halting all Venezuelan oil shipments to Cuba and threatening to slap tariffs on any country that sells oil to Cuba.

As a result, Cuba says it has not received an oil shipment in three months and the country has imposed severe energy rationing, resulting in extended power outages. Much of its economy has ground to a halt. On Monday Cuba's electric grid collapsed, leaving the country of 10 million people without power.

On Sunday, Trump told reporters aboard Air Force One, '"We're talking ​to Cuba, but we're going to do Iran before Cuba."

While more than a dozen U.S. presidents dating back decades have opposed Cuba's Communist government and criticized its human rights record, Washington has honored its pledge not to invade Cuba or support an invasion as part of the agreement with the Soviet Union to resolve the Cuban missile crisis of 1962. 

The White House has yet to detail the legal basis for any possible intervention in Cuba.

The Cuban government did not respond to a request for comment.