AMNA NAWAZ: Crucial talks are due to take place in Washington tomorrow between Vice President J.D.

Vance, Secretary of State Marco Rubio and the foreign ministers of Denmark and Greenland, the strategically important Danish region that President Trump has coveted for years.

His repeated threats to take over the island have prompted warnings that such a move could lead to the breakup of NATO.

Malcolm Brabant reports from Copenhagen.

MALCOLM BRABANT: High noon in Copenhagen, and the guard changes at the main royal palace, as Danes worried that their kingdom is about to be shrunk by a Trumpian heist.

President Trump has been stretching nerves here in Copenhagen this past week by ramping up his rhetoric, but the Danes haven't responded.

They're hoping that quiet diplomacy will neutralize the threat to annex Greenland.

Denmark is backed by NATO allies who believe in the sanctity of Greenland sovereignty.

They fear the president has been emboldened by his Venezuelan operation and will pull the trigger.

DONALD TRUMP, President of the United States: I'm not talking about money for Greenland yet.

I might talk about that.

But, right now, we are going to do something on Greenland, whether they like it or not, because, if we don't do it, Russia or China will take over Greenland.

And we're not going to have Russia or China as a neighbor, OK?

I would like to make a deal, the easy way, but if we don't do it the easy way, we're going to do it the hard way.

MALCOLM BRABANT: Rasmus Jarlov chairs Denmark's Parliamentary Defense Committee.

He says the Danes will be accommodating, but they have some solid red lines.

RASMUS JARLOV, Chair, Denmark Defense Committee: Trump has said that they need to do something on Greenland.

And I would take him at his word, because we don't mind doing something on Greenland.

But what we do mind and what we can never agree to is just handing over Greenland, selling 57,000 Danish citizens to become Americans.

They don't want to do that.

And it's not a matter of price.

They categorically don't want that.

And we're not going to agree to it.

MALCOLM BRABANT: Greenland possesses vast, untapped mineral wealth.

Its strategic importance grows daily as the arctic ice melts, creating maritime passageways across the top of the globe.

The United States' sole military presence is its Pituffik Space Base, used for missile early warning in defense and space surveillance.

Vice President Vance used his visit there last March to pile pressure on Denmark, which is responsible for Greenland's defense and foreign affairs.

J.D.

VANCE, Vice President of the United States: Denmark has not kept pace in devoting the resources necessary to keep this base, to keep our troops, and in my view to keep the people of Greenland safe from a lot of very aggressive incursions from Russia, from China and from other nations.

MALCOLM BRABANT: Lin Mortensgaard is an Arctic specialist at the Danish Institute for International Studies.

She says that, under a 1951 treaty, there's nothing to stop America beefing up its military presence.

LIN MORTENSGAARD, Danish Institute for International Studies: In this defense agreement, the U.S.

has very wide-ranging options for expanding its military presence in Greenland with bases or increasing troops or having new installations, radar installations.

Many different things could be done under this defense agreement.

MALCOLM BRABANT: Last October, Denmark pledged $4.2 billion to boost Greenland's security with ice-breaking patrol vessels and advanced drones.

This commitment, though, is apparently insufficient for President Trump.

TOM CROSBIE, Royal Danish Defense College: There is basically nothing to stop the United States military from staking a claim in Greenland.

So, for example, a single soldier could just walk down the main street of Nuuk and claim that this is America now, but that is something that would be immediately contested.

MALCOLM BRABANT: Associate Professor Tom Crosbie lectures on military operations at the Royal Danish Defense College.

TOM CROSBIE: This is forcing NATO to contemplate its existence and the possibility that it will not exist in the near future.

So this is an absolute existential question for NATO.

It is unprecedented, and I would say it was unimaginable just a few years ago.

It's the most significant challenge NATO has ever encountered.

MALCOLM BRABANT: But, on Monday, NATO Secretary-General Mark Rutte promised action.

MARK RUTTE, NATO Secretary-General: All allies agree on the importance of the Arctic and Arctic security, because we know that, with sea lanes opening up, there is a risk that Russians and the Chinese will be more active.

And, currently, we are working on the next steps to make sure that indeed we collectively protect what is at stake here.

MALCOLM BRABANT: For a different perspective, we turn to Martin Aaholm, a former Danish soldier who, 16 years ago, lost both legs when he knelt on an IED in Helmand Province in Afghanistan.

We met in 2014 when he was performing in an anti-war ballet and reconnected this week as he drove home after delivering a truckload of donated supplies to frontline Ukrainian forces.

MARTIN AAHOLM, Veteran, Danish Armed Forces: As a soldier that had fought for NATO and helped when USA called for Article 5, I feel offended.

I feel hurt.

MALCOLM BRABANT: Despite his injuries, Aaholm has conducted 29 solo missions to Ukraine and he believes the president is on the wrong side of history.

MARTIN AAHOLM: I actually think that Trump is stupid enough to try to attack Greenland.

There's no invading force waiting to invade Greenland.

You protect Greenland with sensors, with satellites, with radars, not with ten thousands of soldiers.

DONALD TRUMP: If you take a look outside of Greenland right now, there are Russian destroyers, there are Chinese destroyers and bigger, there are Russian submarines all over the place.

We're not going to have Russia or China occupy Greenland, and that's what they're going to do if we don't.

So we're going to be doing something with Greenland either the nice way or the more difficult way.

MALCOLM BRABANT: Danish trepidation about the talks in Washington has increased after learning that America's hawkish vice president will be chairing the meeting.

LIN MORTENSGAARD: It's unclear exactly what the agenda is, and we have seen how, for example, meetings in the White House between Trump and Zelenskyy can backfire also.

So this is the delicate balance for Danish and Greenland diplomacy.

MALCOLM BRABANT: And, tonight, the Greenlandic prime minister, Jens-Frederik Nielsen, laid out his red line.

JENS-FREDERIK NIELSEN, Prime Minister of Greenland (through translator): Now we are faced with a geopolitical crisis.

And if we have to choose between the USA and Denmark, here and now, we choose Denmark.

MALCOLM BRABANT: Should they leave Washington empty-handed, the Danes will ask their European allies in NATO to reinforce the defense of Greenland.

A NATO meeting is slated for next Monday.

For the "PBS News Hour," I'm Malcolm Brabant in Copenhagen.