In recent weeks, US President-elect Donald Trump has shown renewed interest in taking control of Greenland, a largely autonomous territory of Denmark in the Arctic and the world’s largest island.

He first indicated an intention to buy Greenland in 2019, during his first term as president, but this week he went further, refusing to rule out economic or military force to take control of it.

Danish and European officials have responded negatively, saying Greenland is not for sale and its territorial integrity must be preserved.

So how could this unusual situation play out, with two Nato allies at odds over a huge territory which is 80% covered with ice but has considerable untapped mineral wealth?

And how could the aspirations for independence among Greenland’s population of 56,000, under Danish control for 300 years, affect the final outcome?

Here we look at four possible scenarios for Greenland’s future.

There is some speculation that Trump’s move is just bluster, a move to get Denmark to boost Greenland’s security in the face of the threat of both Russia and China seeking influence in the region.

Last month, Denmark announced a new $1.5bn (£1.2bn) military package for the Arctic. It had been prepared before Trump’s remarks but the announcement just hours after them was described by the Danish defence minister as an “irony of fate”.

“What was important in what Trump said was that Denmark has to fulfil its obligations in the Arctic or it’s got to let the US do it,” says Elisabet Svane, chief political correspondent for Politiken newspaper.

Marc Jacobsen, associate professor at the Royal Danish Defence College, believes that this is a case of Trump “positioning himself before entering office” while Greenland is using the occasion to gain more international authority, as an important step towards independence.

So even if Trump were to lose further interest in Greenland now, which Professor Jacobsen thinks is the most likely scenario, he has certainly put the spotlight on the issue.

But independence for Greenland has been on the agenda for many years, and some say the debate could even go in the opposite direction.

“I noticed in the last few days the Greenland PM is calmer in his comments – ie. yes, we want independence but in the long run,” says Svane.

There is a general consensus in Greenland that independence will happen eventually, and also that if Greenland votes for it, Denmark will accept and ratify it.

However, it is also unlikely that Greenland would vote for independence unless its people are given guarantees that they can keep the subsidies they currently get from Denmark to pay for things like healthcare and the welfare system.

“The Greenland PM may be up in arms now, but in the event that he actually calls a referendum, he will need some kind of convincing narrative about how to save the Greenland economy and welfare system,” Ulrik Gad, a senior researcher at the Danish Institute for International Studies, told the BBC.

One possible next step is a free association – something like the US currently has with Pacific states the Marshall Islands, Micronesia and Palau.

Denmark has previously opposed this status both for Greenland and for the Faroe Islands, but according to Dr Gad, current Prime Minister Mette Frederiksen is not categorically against it.

“Danish understanding of the Greenland historical experience is way better than it was 20 years ago,” he says, with Denmark accepting colonial responsibility.

The recent discussions “might persuade [Frederiksen] to say – better to keep Denmark in the Arctic, keep some kind of connection to Greenland, even if it’s a looser one”, he adds.

But even if Greenland is able to get rid of Denmark, it has become clear in recent years that it can’t get rid of the US. The Americans never really left after taking control of the island in World War Two, and see it as vital for their security.

An agreement in 1951 affirmed Denmark’s basic sovereignty of the island but, in effect, gave the US whatever it wanted.

Dr Gad said that Greenland officials had been in contact with the last two US administrations about Washington’s role.

“They now know the US will never leave,” he said.

There has been speculation that Trump’s economic rhetoric is potentially the biggest threat to Denmark – with the US drastically increasing tariffs on Danish, or even EU, goods, forcing Denmark into concessions of some kind over Greenland.

Professor Jacobsen says Danish governments have been preparing for that, and not just because of the Arctic territory.

Trump has been threatening universal 10% tariffs on all US imports which could, among other things, significantly disrupt European growth, and some Danish and other European companies are now considering setting up manufacturing bases in the US.

Possible options for raising tariffs include by invoking the 1977 International Emergency Economic Powers Act (IEEPA), Benjamin Cote of international law firm Pillsbury told the website MarketWatch.

One of the main Danish industries potentially affected by this is pharmaceuticals. The US receives products such as hearing aids and most of its insulin from Denmark, as well as the diabetes drug Ozempic, made by the Danish company Novo Nordisk.

Analysts say the hike in prices that would result from these measures would not find favour with the US public.

The “nuclear option” seems far-fetched, but with Trump failing to rule out military action it has to be considered.

Essentially, it wouldn’t be hard for the US to take control, given that they already have bases and plenty of troops in Greenland.

“The US has de facto control already,” says Professor Jacobsen, adding that Trump’s remarks seemed ill-informed and he didn’t understand the point of them.

That said, any use of military force by Washington would create an international incident.

“If they invade Greenland, they invade Nato,” says Svane. “So that’s where it stops. Article 5 would have to be triggered. And if a Nato country invades Nato then there’s no Nato.”

Dr Gad says Trump sounds like Chinese President Xi Jinping talking about Taiwan or Russia’s Vladimir Putin talking about Ukraine.

“He’s saying it’s legitimate for us to take this piece of land,” he says. “If we take him really seriously this is a bad omen for the whole of the Western alliance.”

Additional reporting by George Sandeman