France and Germany on Wednesday warned Donald Trump against threatening "sovereign borders" after the US president-elect refused to rule out military action to take Greenland, an autonomous territory of European Union member Denmark.

"There is no question of the EU letting other nations in the world, whoever they may be... attack its sovereign borders," French Foreign Minister Jean-Noel Barrot told France Inter radio.

"We are a strong continent. We need to strengthen ourselves more," he added.

In Berlin, German government spokesman Steffen Hebestreit said in response to Trump's remarks that "as always, the firm principle applies... that borders must not be moved by force".

Barrot described Greenland as "European territory". Greenland is associated with the European Union through Denmark, of which it is a self-governing territory, but withdrew from the European bloc in 1985 after securing autonomy.

Trump set off new alarm on Tuesday at a press conference when he refused to rule out military intervention over the Panama Canal and Greenland, both of which he has said he wants the United States to control.

"We need Greenland for national security purposes," he declared.

His comments coincided with a private visit by his son Donald Trump Jr. to the mineral- and oil-rich autonomous Danish territory on Tuesday.

"If you ask me: 'is the United States going to invade Greenland?' the answer is no," said Barrot.

But he added: "We have entered an era that is seeing the return of the law of the strongest."

"Should we be intimidated? Should we be overcome with worry? Evidently, no. 

"We need to wake up and reinforce ourselves, militarily, in competition, in a world where the law of the strongest prevails."

Barrot said he believed that the United States is "inherently not imperialistic" and said he "did not believe" that it is changing.

However French government spokeswoman Sophie Primas told reporters after a cabinet meeting that there was a "form of imperialism" in Trump's comments.

"Today we are seeing the rise in blocs, we can see this as a form of imperialism, which materialises itself in the statements that we saw from Mr Trump on the annexation of an entire territory."

"More than ever, we and our European partners need to be conscious, to get away from a form of naivety, to protect ourselves, to rearm," she added.

The German government spokesman refused to be drawn on whether Berlin takes Trump's threats against NATO allies Denmark and Canada seriously.

"I don't want to assess" the comments, Hebestreit told a news conference, adding only that the German government had "taken note" of them.

At the news conference, Trump called the border with the United States' northern neighbour Canada an "artificially drawn line" and promised to rename the Gulf of Mexico the "Gulf of America."

Denmark says 'open to dialogue' with US on the Arctic 

Denmark said on Wednesday that it is open to talks with the United States to safeguard US interests in the Arctic.

Danish Foreign Minister Lars Lokke Rasmussen told reporters that the Danish Realm -- which includes Denmark, Greenland and the Faroe Islands -- is "open to a dialogue with the Americans on how we can cooperate, possibly even more closely than we already do, to ensure that American ambitions are fulfilled."

Lokke Rasmussen noted that the United States and NATO had "legitimate" interests in the region because of international events.

"In conjunction with the melting of the Arctic and new shipping lanes opening up, we are unfortunately also seeing an increase in great power rivalry. We see a Russia that is arming itself. We see a China that is also starting to take an interest," the foreign minister said.

The top diplomat urged calm amid the new frenzy.

"I try to deal with the realities, and I think we should all do ourselves a favour by getting our heart rate down a bit," he said.

Danish Prime Minister Mette Frederiksen told TV2 television on Tuesday she did not believe Trump's pursuit of Greenland would ever include military force.

"I don't have the fantasy to imagine that it'll ever get to that," she said, calling for cool heads to prevail.