Denmark on Sunday called on the United States to stop "threatening" Greenland, as President Donald Trump told US media he "absolutely" needed the territory, a day after Washington seized the leader of Venezuela.

Washington's military intervention in Venezuela has reignited fears for Greenland, which Trump has repeatedly made clear he wants to become an annexed part of the United States.

Those fears were underscored by Trump's comments to The Atlantic magazine and a social media post by the wife of his most influential aide showing Greenland in the colours of the US flag.

"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," Danish Prime Minister Mette Frederiksen said in a statement late on Sunday.

She called on Washington to stop "threatening its historical ally".

The United States's European allies were rattled by Trump sending in his military on Saturday to attack Caracas and grab Venezuelan president Nicolas Maduro, who is now being held in New York.

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

In Greenland's case, Trump has claimed that making the Danish territory part of the United States would serve US national security interests, given its strategic location on the Arctic.

Greenland is also rich in key critical minerals used in high-tech sectors. Asked in a telephone interview with The Atlantic about the implications of the Venezuela military operation for Greenland, Trump said that it was up to others to decide, according to the magazine on Sunday.

"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."

Late on Saturday, Katie Miller – wife of Trump's deputy chief of staff Stephen Miller – posted the contentious image of the Danish autonomous territory in the colours of the US flag on her X feed.

Her post had a single word above it: "SOON".

Greenland's Prime Minister Jens-Frederik Nielsen called the 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 stated on X.

But he also said that "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," he said.

Denmark's ambassador to the US, Jesper Moeller Soerensen, reacted earlier on Sunday with his own post saying "we expect full respect for the territorial integrity" of Denmark, above a link to Katie Miller's image. (AFP)