US Vice-President JD Vance says Greenland is "critical" for the defence of the US and the world against possible Russian or Chinese missile attacks - and that Europe and Denmark have "not done a good job" in securing the area.

Vance told Fox News that they had not only under-invested in Greenland's defences, but also failed to engage with President Donald Trump's argument over the issue.

US officials are "actively" discussing a potential offer to buy Greenland - a semi-autonomous Danish territory - the White House said on Wednesday, a day after suggesting military action to annex it to the US was also an option.

Denmark, a fellow Nato member, has warned this would spell the end of the alliance.

Both Greenland and Denmark have repeatedly stressed the island is not for sale.

Despite being the most sparsely populated territory, Greenland's location between North America and the Arctic makes it well placed for early warning systems in the event of missile attacks, and for monitoring vessels in the region.

Pituffik Space Base, formerly known as Thule Air Base, has been operated by the US since World War Two.

In recent years, there has also been increased interest in Greenland's natural resources - including rare earth minerals, uranium and iron - which are becoming easier to access as its ice melts due to climate change. Scientists think it could also have significant oil and gas reserves.

"People do not realise that the entire missile defence infrastructure is partially dependent on Greenland," Vance said in his interview on Wednesday.

"If God forbid the Russians and the Chinese - not saying they're going to - but if, God forbid, somebody launched a nuclear missile into our continent, they launched a nuclear missile at Europe, Greenland is a critical part of that missile defence.

"So you ask yourself, 'have the Europeans, have the Danes done a proper job of securing Greenland and of making sure it can continue to serve as an anchor for world security and missile defence?' And the answer is obviously they haven't," he said.

Concerns over the future of the territory resurfaced after Trump's use of military force against Venezuela on Saturday to seize its President Nicolás Maduro.

Trump previously made an offer to buy the island in 2019, during his first presidential term, only to be told it was not for sale.

US Secretary of State Marco Rubio said on Wednesday that he would hold talks with Denmark next week.

A day earlier, European leaders issued a joint statement rallying behind Denmark.

"Greenland belongs to its people, and only Denmark and Greenland can decide on matters concerning their relations," the leaders of France, the UK, Germany, Italy, Poland, Spain and Denmark said in a joint statement.

Stressing they were as keen as the US on Arctic security, the European signatories said this must be achieved by Nato allies, including the US, "collectively".

They also called for "upholding the principles of the UN Charter, including sovereignty, territorial integrity and the inviolability of borders".

Aaja Chemnitz, one of two MPs in the Danish parliament representing Greenland, told the BBC that the comments from the Trump administration were "a clear threat".

"It's completely disrespectful from the US side to not rule out annexing our country and to annex another Nato ally," she said.

But Chemnitz said she saw this as unlikely and that instead, "what we are going to see is that they will put pressure on us in order to make sure that they will take over Greenland over time".

Aleqatsiaq Peary, a 42-year-old Inuit hunter living in Greenland's remote northerly town of Qaanaaq, appeared indifferent to the potential of US ownership.

"It would be switching from one master to another, from one occupier to another," he told the BBC. "We are a colony under Denmark. We are already losing a lot from being under the Danish government."

Saying that he did not have "time for Trump", he added that people were "in need". Hunters like him, he explained, hunted with dogs on the sea ice and fish "but the sea ice is melting and hunters cannot make a living anymore".

Additional reporting by Adrienne Murray in Copenhagen