Trump has signalled his desire for the Arctic island, which is believed to hold large untapped mineral and oil reserves, to become part of the United States.

Trump has talked for years about a possible deal to take over the Danish autonomous territory, and told reporters on Saturday he believed the United States would "get Greenland".

He has insisted his country needs Greenland for "international security".

Frederiksen met with German Chancellor Olaf Scholz in Berlin on Tuesday.

After speaking about Russia's war in Ukraine, Scholz stressed that "borders must not be moved by force" and added the English-language phrase: "To whom it may concern."

The chancellor said "the times we live in are challenging" and require a strong Europe and NATO. He stressed that "Denmark and Germany are strong partners and close friends".

In Paris, Frederiksen met with French President Emmanuel Macron, before heading to Brussels later in the day to see NATO Secretary General Mark Rutte.

Tuesday's visits followed a weekend Nordic summit where leaders all "shared the gravity of the situation", Frederiksen said.

- Denmark boosts Arctic security -

Denmark announced Monday that it would spend 14.6 billion kroner ($2 billion) to bolster security in the strategic Arctic region.

It said it would send three new frigates to the region, as well as long-distance drones equipped with advanced imaging capabilities. It would also reinforce its satellite capabilities.

Greenland lies between the United States and Europe, a region of increasing strategic value as the melting of Arctic sea ice opens up new shipping routes.

Officials in the territory, which depends heavily on Denmark for subsidies, have long been pushing for independence but have said they are open to doing business with the US.

A day after Trump was sworn in as president, Greenland Prime Minister Mute Egede insisted Greenlanders "don't want to be American".

In mid-January, Frederiksen reportedly spoke to Trump by telephone, stressing that it was up to Greenland to determine its future.

According to European sources cited by the Financial Times, Danish officials described the conversation as "horrendous", and that Trump's interest in Greenland was "serious, and potentially very dangerous".

The US president, who has not excluded a possible military intervention to annex the island, reportedly threatened Denmark with tariffs over the issue.

The United States is the small Scandinavian country's main export market.

- 'Worrying time' -

Greenland's trade and justice minister Naaja Nathanielsen told AFP on Monday the Greenlandic people were living through a "worrying time" and were "concerned" about Trump's statements.

"As a government our job is not to panic and figure out what the actual demands are," Nathanielsen said.

"If it is about military presence, the US has been here for 80 years, we are not opposed to that. If it is about the minerals, it is an open market," she added.

But, she warned, "if it is about expansionism, we are a democracy, we are allies and we ask our allies to respect our institutions."

The European Union's top military official said Saturday said troops from EU countries could be based in Greenland.

"In my view, it would make perfect sense not only to station US forces in Greenland, as is currently the case, but also to consider stationing EU soldiers there," Robert Brieger, chairman of the European Union Military Committee told German newspaper Welt am Sonntag.

France's Foreign Minister Jean-Noel Barrot did not rule out the possibility of European troops in Greenland.

"Why not, since it is a matter of security," Barrot told Sud Radio on Tuesday.

He stressed however that "that is not the wish expressed by Denmark, but it is a possibility."