A day after the audacious US military operation in Venezuela, President Donald Trump renewed his calls for an American takeover of the Danish territory of Greenland for the sake of American security interests and threatened military action on Colombia for facilitating the global sale of cocaine, while his top diplomat declared the communist government in Cuba is “in a lot of trouble”.

The comments from Trump and Secretary of State Marco Rubio after the ouster of Venezuela's Nicolás Maduro underscore that Washington is serious about taking a more expansive role in the Western Hemisphere.

With thinly veiled threats, Trump is rattling hemispheric friends and foes alike, spurring a pointed question around the globe: who's next?

Trump, in his administration's national security strategy published last month, laid out restoring "American preeminence in the Western Hemisphere" as a central guidepost for his second go-around in the White House.

Trump has also pointed to the 19th century Monroe Doctrine, which rejects European colonialism, as well as the Roosevelt Corollary – a justification invoked by the United States in supporting Panama’s secession from Colombia, which helped secure the Panama Canal Zone for the US – as he's made his case for an assertive approach to American neighbours and beyond.

Concern is simmering in Cuba, one of Venezuela’s most important allies and trading partners, as Rubio issued a new stern warning to the Cuban government.

US-Cuba relations have been hostile since the 1959 Cuban revolution.

Rubio, in an appearance on NBC's “Meet the Press,” said Cuban officials were with Maduro in Venezuela ahead of his capture.

“It was Cubans that guarded Maduro,” Rubio said.

“He was not guarded by Venezuelan bodyguards. He had Cuban bodyguards.”

The secretary of state added that Cuban bodyguards were also in charge of “internal intelligence” in Maduro’s government, including “who spies on who inside, to make sure there are no traitors”.

Trump said that the Cuban economy, battered by years of a US embargo, was in tatters and would slide further now with the ouster of Maduro, who provided the Caribbean island with subsidised oil.

As he made his way back to Washington on Sunday evening, he also put Venezuela's neighbour, Colombia, and its leftist president, Gustavo Petro, on notice, saying Colombia was “run by a sick man who likes making cocaine and selling it to the United States.”

The Trump administration imposed sanctions in October on Petro, his family and a member of his government over accusations of involvement in the global drug trade.

Colombia is considered the epicentre of the world's cocaine trade.

Trump began his months-long pressure campaign on Maduro by ordering dozens of lethal strikes on alleged drug smuggling boats launched from Venezuela in the Caribbean.

He eventually expanded the operations to also target suspected vessels in the eastern Pacific that came from Colombia.

The United States in September also added Colombia, the top recipient of American assistance in the region, to a list of nations failing to co-operate in the drug war for the first time in almost 30 years.

The designation led to a slashing of US assistance to the country.

“He’s not going to be doing it for very long,” Trump said of Petro on Sunday.

“He has cocaine mills and cocaine factories. He’s not going to be doing it.”

Asked whether he might order the United States to conduct an operation against Colombia, Trump replied, “It sounds good to me.” (AP)