On Wednesday, United States President Donald Trump made clear to other world leaders in Davos, Switzerland, that he was unflinching in his demand to acquire Greenland, even as he said for the first time that he did not plan for the US to take the land by force.

Trump, who talked up his tariff-based negotiation strategy, cited Greenland’s strategic position between the US, Russia and China as the main reason he wants to acquire the territory.

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Retelling the US history with Greenland and Denmark, Trump said, during World War II, “we saved Greenland and successfully prevented our enemies from gaining a foothold in our hemisphere”.

This much is accurate: After Germany invaded Denmark, the US assumed responsibility for Greenland’s defence and established a military presence on the island that remains today, albeit in diminished scope.

But Trump overstepped when he said, after World War II, “we gave Greenland back to Denmark”.

“All the United States is asking for is a place called Greenland, where we already had it as a trustee, but respectfully returned it back to Denmark not long ago,” he said.

Although the US defended Greenland during World War II, it never possessed the nation, and so could not have given it back. Experts have told PolitiFact that Greenland’s status as part of Denmark is not in question, and has not been for more than a century.

Denmark’s colonisation of Greenland dates to the 1720s. In 1933, an international court settled a territorial dispute between Denmark and Norway, ruling that as of July 1931, Denmark “possessed a valid title to the sovereignty over all Greenland”.

After the 1945 approval of the United Nations Charter – the organisation’s founding document and the foundation of much of international law – Denmark incorporated Greenland through a constitutional amendment and gave it representation in the Danish Parliament in 1953. Denmark told the UN that any colonial-type status had ended; the UN General Assembly accepted this change in November 1954. The US was among the nations that voted to accept Greenland’s new status.

Since then, Greenland has, incrementally but consistently, moved towards greater autonomy.

Greenlandic political activists successfully pushed for and achieved home rule in 1979, which established its parliament. Today, Greenland is a district within the sovereign state of Denmark, with two elected representatives in Denmark’s Parliament.

What about Iceland?

Four times in the Davos speech, Trump referred to Iceland instead of Greenland.

“Our stock market took the first dip yesterday because of Iceland,” Trump said. “So Iceland has already cost us a lot of money, but that dip is peanuts compared to what it’s gone up, and we have an unbelievable future.”

US markets reacted negatively to Trump’s Greenland comments the day before his Davos speech, falling about 2 percent in value.

But in recent weeks, Trump has said nothing about acquiring Iceland, an independent island nation with nearly 400,000 residents, located east of Greenland.

In an X post following Trump’s Davos address, the White House press secretary criticised a reporter for posting that Trump “appeared to mix up Greenland and Iceland” several times. Karoline Leavitt said Trump’s “written remarks referred to Greenland as a ‘piece of ice’ because that’s what it is”. Although Trump did call Greenland a “very big piece of ice”, he also separately mentioned “Iceland”.

Traditionally, Icelanders have maintained strong ties to the US, dating back to World War II, when Reykjavik invited US troops into the country. In 1949, Iceland became a founding member of NATO, and in 1951, the two countries signed a bilateral defence agreement that still stands.

Its location – between the Arctic and North Atlantic oceans, a strategic naval choke point in the Greenland-Iceland-United Kingdom gap – means that Iceland, despite its lack of a standing military, is geographically important for both North America and Europe.

In 2006, the US gave up its permanent troop presence at the Keflavík airbase – a 45-minute drive south of the capital, Reykjavik – but US troops still rotate through. Icelandic civilians now handle key NATO tasks such as submarine surveillance and operations at four radar sites on the nation’s periphery. Iceland also makes financial contributions to NATO trust funds and contributes a small number of technical and diplomatic personnel to NATO operations.

Trump’s pick for ambassador to Iceland, former Republican Congressman Billy Long, attracted criticism earlier this month when he was overheard saying Iceland should become a US state after Greenland, and that he would serve as governor.

Long apologised during an interview with Arctic Today.

“There was nothing serious about that. I was with some people, who I hadn’t met for three years, and they were kidding about Jeff Landry being governor of Greenland, and they started joking about me. And if anyone took offence to it, then I apologise,” Long told the publication. Trump has tapped Landry, Louisiana’s Republican governor, to be the US envoy to Greenland.

Silja Bara R Omarsdottir, an international affairs professor who now serves as rector, or president, of the University of Iceland, told the Tampa Bay Times in August that newfound attention to Iceland’s security, including concerns over Russia’s invasion of Ukraine for the rest of Europe, is “definitely very noticeable at the political level”.

Multiple analysts in Iceland told the daily, only half-jokingly, that the key to surviving the Trump era has been to remain out of sight, something Greenland, for whatever reason, was unlucky enough not to be able to do.

“You could say Icelandic policy towards the US has been to try to keep under the radar,” said Pia Elisabeth Hansson, director of the Institute of International Affairs at the University of Iceland.