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.

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.

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

Aaja Chemnitz, one of two MPs in the Danish parliament representing Greenland, called the threats from the Trump administration completely disrespectful.