Washington's military intervention in Venezuela has reignited fears for Greenland, which Trump has repeatedly said he wants to annex, given its strategic location in the Arctic.

While aboard Air Force One en route to Washington, Trump reiterated the goal.

"We need Greenland from the standpoint of national security, and Denmark is not going to be able to do it," he said in response to a reporter's question.

"We'll worry about Greenland in about two months... let's talk about Greenland in 20 days."

Over the weekend, the Danish prime minister called on Washington to stop "threatening its historical ally".

"I have to say this very clearly to the United States: it is absolutely absurd to say that the United States should take control of Greenland," Prime Minister Mette Frederiksen said in a statement.

She also noted that Denmark, "and thus Greenland", was a NATO member protected by the agreement's security guarantees.

Trump rattled European leaders by attacking Caracas and grabbing Venezuelan president Nicolas Maduro, who is now being detained in New York.

Trump has said the United States will now "run" Venezuela indefinitely and tap its huge oil reserves.

Asked in a telephone interview with The Atlantic about the implications of the Venezuela military operation for mineral-rich Greenland, Trump said it was up to others to decide.

"They are going to have to view it themselves. I really don't know," Trump was quoted as saying.

He added: "But we do need Greenland, absolutely. We need it for defence."

Hours later, former aide Katie Miller, the wife of Trump's most influential adviser, drew ire by posting an image of Greenland in the colours of the US flag, captioning it "SOON".

Greenland's Prime Minister Jens-Frederik Nielsen called Miller's post "disrespectful".

"Relations between nations and peoples are built on mutual respect and international law -- not on symbolic gestures that disregard our status and our rights," he wrote on X.

But he also said "there is neither reason for panic nor for concern. Our country is not for sale, and our future is not decided by social media posts".

Stephen Miller is widely seen as the architect of much of Trump's policies, guiding the president on his hardline immigration policies and domestic agenda.

Denmark's ambassador to the United States, Jesper Moeller Soerensen, offered a pointed "friendly reminder" in response to Katie Miller's post that his country has "significantly boosted its Arctic security efforts" and worked together with Washington on that.

"We are close allies and should continue to work together as such," Soerensen wrote.

Katie Miller was deputy press secretary under Trump at the Department of Homeland Security during his first term.

She later worked as communications director for then-vice president Mike Pence and also acted as his press secretary.

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