“The people of Greenland do not want to become American,” Mia Chemnitz tells the BBC. “We are not for sale.”

The 32-year-old business owner in the Greenlandic capital Nuuk reflects the sentiments of many who spoke to the BBC about how they felt about recent rhetoric from the Trump administration.

The White House has said it was “actively” discussing an offer to buy the territory that has for centuries belonged to Denmark. US President Donald Trump and his officials had earlier intimated a willingness to take it by force if necessary.

This has been met with nervousness and opprobrium among Greenlanders – both on the world’s largest island and elsewhere.

This nervousness has only grown since the US took Venezuela’s President Nicolás Maduro from his residence in Caracas to New York on drug-trafficking and narco-terrorism charges in an unprecedented military move.

Almost immediately after, the wife of a senior White House staffer indicated that Greenland was next.

“That’s when it stopped feeling abstract,” says Tupaarnaq Kopeck, 40, who moved to Canada – another place Trump has threatened to annex – for family and work.

“For the first time, I contacted my sister in Greenland and told her that if the unthinkable ever became reality, they would have a place to stay with us.”

Aaja Chemnitz, one of two MPs in the Danish parliament representing Greenland, says the comments from the Trump administration are “a clear threat” that she was “appalled” by.

“It’s completely disrespectful from the US side to not rule out annexing our country and to annex another Nato ally,” she says.

Greenland is the world’s most sparsely populated territory. With much of the Arctic island covered by ice, most of the population lives in Nuuk and the surrounding south-western coastline.

But it is strategically significant to the US – which is why it has had a military presence there since World War Two.

Greenland’s location between North America and the Arctic makes it well placed for early warning systems in the event of missile attacks.

More recently, there has also been increased interest in Greenland’s natural resources, including rare earth minerals, which are becoming easier to access as its ice melts due to climate change.

“It’s not fun being 56,000 people and having these threats – if you can call them that – from a giant like the US,” says Masaana Egede, editor of Greenlandic newspaper Sermitsiaq.

“The citizens of Greenland are nervous about this, because this is not something that we take lightly.”

Experts generally agree that a military takeover of Greenland would be an easy undertaking for the US – but that the geopolitical fallout would effectively end the Nato alliance.

After the issue of Greenland’s ownership was raised anew by the White House, six European allies issued a statement saying its future should be decided by its people – something Mia says she is grateful for.

But she worries this will matter little to the US “if it’s not backed with consequences and actions”.

“As a Greenlander, I can’t help but wonder: what are we worth to these allies? To what lengths are they willing to go to protect us?”

Tupaarnaq says: “Respect is about more than alliances on paper. When powerful nations talk about you instead of with you, that respect disappears very quickly.”

The Trump administration has stressed its intention was to buy Greenland from Denmark – despite Copenhagen reiterating the territory was not for sale – while retaining a military intervention as an option.

Aaja sees annexation by force as unlikely – 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”.

Polling consistently shows that Greenlanders generally favour eventual independence from Denmark but oppose being owned by the US. The territory is largely self-governing, with control of foreign affairs and defence retained by Copenhagen.

This is perhaps why Aleqatsiaq Peary, a 42-year-old Inuit hunter living in the remote northerly town of Qaanaaq, seemed unfazed by the prospect of US ownership.

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

But he says: “I don’t have time for Trump. Our people are in need,” explaining hunters like him hunt with dogs on the sea ice and fish, “but the sea ice is melting and hunters cannot make a living anymore”.

For Sermitsiaq editor Masaana, the rhetoric from the US is pushing a fallacious binary choice.

“We really have to try to avoid getting the story going to a place where it’s Greenland that has to decide between the US and Denmark, because that is not the choice that the Greenlandic people want.”

For others, who see the strong relationship Greenland already has with the US being soured, there is a clear sense of indignation.

“People in Greenland are getting really irritated with this,” says Christian Keldsen of the Greenland Business Association.

“Greenlanders are welcoming and open-hearted, it’s the best thing about the country. But now with this, some people are scared.”

Greenland is open for business with the US, Christian stresses, noting that there are new direct flights from Greenland to New York – a sure sign “they don’t need to take us over”.

“We are a well-functioning democracy and our government has a strong mandate,” Mia says. “We are a Nato ally and the US has had military bases in Greenland for over 70 years – and still has the right to establish and run new and more.

“As it has been stated from Greenland before: we are not for sale, but we’re open for business.”