Greenland and Denmark on Sunday expressed their distaste after the wife of President Donald Trump's most influential aide posted a social media picture of Greenland painted in the colours of the US flag.

Katie Miller -- wife of Trump's deputy chief of staff Stephen Miller -- put the contentiously altered image of the Danish autonomous territory on her X feed late Saturday, after the US military operation against Venezuela.

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".

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.

Trump has repeatedly made clear that he wants Greenland to become an annexed part of the United States.

Moves edging towards that goal by his government -- including his appointment of an envoy to the Danish territory -- have drawn the ire of both Copenhagen and the European Union.

- 'Friendly reminder' -

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.

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 by US authorities 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.

"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 defense."

Denmark's ambassador gave a pointed "friendly reminder" in response to Katie Miller's post that his country -- a NATO member -- has "significantly boosted its Arctic security efforts" and worked together with the US 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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AFP

Greenland slams 'disrespectful' pic posted by Trump aide's wife