Copenhagen, Denmark - Denmark's prime minister warned Monday that any US move to follow through with President Donald Trump's threats of annexing Greenland would spell the end of NATO.

The US coup in Venezuela has reignited fears about Trump's designs on the autonomous Danish territory, which has untapped rare earth deposits and could be a vital player as polar ice melts, opening up new shipping routes.

"We need Greenland from the standpoint of national security, and Denmark is not going to be able to do it," Trump said Sunday.

The next day, top advisor Stephen Miller poured more fuel on the fire by suggesting on CNN that Denmark had no right to assert control over the island.

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"The United States should have Greenland as part of the United States. There's no need to even think or talk about this in the context that you're asking, of a military operation," he told Jake Tapper.

"Nobody's going to fight the United States militarily over the future of Greenland."

Miller wife had over the weekend also posted an online image of Greenland in the colors of the US flag with the caption "SOON," sparking angry rebukes.

In response, Greenland's Prime Minister Jens-Frederik Nielsen told Trump to back off, while Europe rushed to back Denmark.

In Copenhagen, Prime Minister Mette Frederiksen told the TV2 network: "If the United States decides to military attack another NATO country, then everything would stop – that includes NATO and therefore post-World War II security."

Greenland is on the shortest route for missiles between Russia and the US, and Washington already has a military base there.

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With the situation in Venezuela more pressing, "we'll worry about Greenland in about two months," Trump quipped Sunday.

Nielsen told Trump on social media: "Enough is enough. No more pressure. No more insinuations. No more fantasies of annexation."

On Monday, he called for renewed contact with the US and urged against panic.

"The situation is not such that the United States can conquer Greenland. That is not the case. Therefore, we must not panic. We must restore the good cooperation we once had," Nielsen said in Nuuk.

Aaja Chemnitz, who represents Greenland in the Danish parliament, accused Trump of "spreading lies about Chinese and Russian warships" posing an immediate danger.

"The people of Greenland should go into preparation mode," she told AFP, adding that Greenlanders needed to start taking Trump much more seriously.

On the streets of Copenhagen, people expressed bewilderment at Trump's threats.

"I think it's a little crazy that he can say those things," said Frederik Olsen.

"He has all the access he wants for the troops," said Christian Harpsoe. "I see no need. You cannot compare this to Venezuela."