Denmark's prime minister warned Monday that any US move to take Greenland by force would destroy 80 years of transatlantic security links, after President Donald Trump repeated his desire to annex the mineral-rich Arctic territory.

Washington's military intervention 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," the US leader said Sunday.

In response, Greenland's Prime Minister Jens-Frederik Nielsen told Trump to back off, while several European countries and the European Union rushed to back Denmark, which has urged Washington to stop threatening a NATO ally.

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 United States, and Washington already has a military base there.

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: "That's enough now. No more pressure. No more insinuations. No more fantasies of annexation."

"We are open to dialogue," he said. "But this must happen through the proper channels and with respect for international law."

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.

'China threat'

Trump rattled European leaders by seizing Venezuelan president Nicolas Maduro, who is now detained in New York.

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

The US leader has similarly ramped up pressure on Greenland over recent months, saying in December that Russian and Chinese ships were "all over" the territory's coast.

The foreign ministry in Beijing hit back on Monday, urging Washington to "stop using the so-called China threat as an excuse to seek personal gain".

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

"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, 56.

"He has all the access he wants for the troops," said Christian Harpsoe, 46. "I see no need. You cannot compare this to Venezuela."

'Disrespectful'

The controversy drew statements of support from around Europe. EU foreign policy spokesperson Anitta Hipper told reporters the bloc was committed to defending the territorial integrity of its members.

British Prime Minister Keir Starmer said "only Greenland and the Kingdom of Denmark" could decide the territory's future -- sentiments reflected in statements from the leaders of Finland, Sweden and Norway.

France's foreign ministry spokesman Pascal Confavreux told local TV that "borders cannot be changed by force" and added that his country felt "solidarity" with Denmark.

The flare-up came after former Trump aide Katie Miller posted an online image Saturday of Greenland in the colours of the US flag with the caption "SOON".

Nielsen labelled the post "disrespectful". Denmark's Frederiksen on Sunday called on Washington to stop "threatening its historical ally" and said US claims on Greenland were "absurd".

Miller is the wife of top Trump adviser Stephen Miller, seen as the guiding force behind the president's hardline immigration policies.

Asked by CNN on Monday if the United States would rule out military intervention in Greenland, Stephen Miller questioned what the "basis" is of "having Greenland as a colony of Denmark".

"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 said in the televised interview.

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