The US bombardment of Venezuela and the capture of its president, Nicolás Maduro, have renewed fears of an American takeover of Greenland, as members of Donald Trump’s Maga movement gleefully set their sights on the Danish territory after the attack in South America.

Just hours after the US military operation in Venezuela, the rightwing podcaster Katie Miller – the wife of Stephen Miller, Donald Trump’s powerful deputy chief of staff for policy – posted on X a map of Greenland draped in the stars and stripes with the caption: “SOON.”

The threat to annex the mineral-rich territory, which is part of the Nato alliance, drew immediate outrage from Danes.

Copenhagen’s ambassador to the US, Jesper Møller Sørensen, reposted Miller’s provocation with a “friendly reminder” of the longstanding defence ties between the two countries.

“We are close allies and should continue to work together as such. US security is also Greenland’s and Denmark’s security,” he said. “The Kingdom of Denmark and the United States work together to ensure security in the Arctic.”

He said Denmark had increased defence spending in 2025, committing $13.7bn (£10.2bn) “that can be used in the Arctic and North Atlantic. Because we take our joint security seriously.”

He added: “And yes, we expect full respect for the territorial integrity of the Kingdom of Denmark.”

Trump recently named Jeff Landry, the governor of Louisiana, as a special envoy to Greenland. Landry, a former state attorney general, thanked Trump for his appointment in December, saying it was “an honour to serve you in this volunteer position to make Greenland a part of the US”.

On Saturday, Landry welcomed Trump’s toppling of Maduro by force.

“Having served as a sheriff’s deputy and AG, I have seen the devastating effects of illegal drugs on American families. With over 100k opioid-related deaths annually, I am grateful to see a President finally take real action in the war on drugs,” he posted on X.

“Thank you @realDonaldTrump for holding individuals like Maduro accountable.”

Since taking office a year ago, Trump has rattled European allies with his stated designs on Greenland, which is seen as strategically important for defence and as a future source of mineral wealth. It is home to the US’s most northerly military base, at Pituffik, which Trump’s vice-president, JD Vance, visited in March.

The US president has refused to rule out military action to gain control of the territory at a time when the US, China and Russia are jockeying for power in the Arctic, a prospect that has triggered widespread condemnation and disquiet on the island itself.

“I don’t rule it out. I don’t say I’m going to do it, but I don’t rule out anything. No, not there. We need Greenland very badly,” Trump told the US broadcaster NBC in May when asked about a potential takeover by force.

“Greenland is a very small amount of people, which we’ll take care of, and we’ll cherish them, and all of that. But we need that for international security.”

In response to a constant drumbeat of threats against the territory, the Danish Defence Intelligence Service last month labelled the US a security risk in a dramatic change in transatlantic relations.

The prime ministers of Denmark and Greenland, Mette Frederiksen and Jens-Frederik Nielsen, said at the time: “We have said it very clearly before. Now we say it again. National borders and the sovereignty of states are rooted in international law … You cannot annex other countries.”

The vast majority of Greenland’s 57,000 inhabitants want to become independent from Denmark but have no wish to become part of the US, according to a poll in January. The territory has had the right to declare independence since 2009.

Jennifer Kavanagh, the director of military analysis at Defense Priorities, a thinktank that advocates restraint in US foreign policy, said she had long dismissed Trump’s sabre-rattling toward Greenland.

“Now I’m not so sure,” she said. “It wouldn’t be that hard for the US to put a couple hundred or a couple thousand troops inside of Greenland, and it’s not clear to me who could do anything about it.”

Agence France-Presse contributed to this report.