France has said the European Union will not allow other nations to attack its "sovereign borders" after US President-Elect Donald Trump refused to rule out using military force to seize Greenland.

On Tuesday, Trump reiterated his desire to acquire the autonomous Danish territory, saying it was "critical" for national and economic security.

French Foreign Minister Jean-Noël Barrot told French radio "There is obviously no question that the European Union would let other nations of the world attack its sovereign borders, whoever they are".

Barrot said he did not believe the US was going to invade the vast Arctic island, but he was clear the EU should not let itself be intimidated.

Trump has repeatedly expressed an interest in buying Greenland, having mooted the idea during his first term as president.

Denmark, a long-time US ally, has made clear that Greenland is not for sale and that it belongs to its inhabitants.

Greenland's prime minister, Mute Egede, is pushing for independence and has also made clear the territory is not for sale. He was visiting Copenhagen on Wednesday.

Trump made the remarks at a free-wheeling news conference at his Mar-a-Lago estate in Florida, less than two weeks before he is sworn in for his second term as president.

Asked if he would rule out using military or economic force in order to take over Greenland or the Panama Canal, Trump said: "No, I can't assure you on either of those two.

"But I can say this, we need them for economic security."

Greenland has been home to a US radar base since the Cold War and has long been strategically important for Washington.

Trump suggested the island was crucial to military efforts to track Chinese and Russian ships, which he said are "all over the place".

"I'm talking about protecting the free world," he told reporters.

Speaking to France Inter radio, Barrot said: "If you're asking me whether I think the United States will invade Greenland, my answer is no.

"Have we entered into an era that sees the return of the survival of the fittest? Then the answer is yes.

"So, should we allow ourselves to be intimidated and overcome with worry, clearly not. We must wake up, build up our strength."

Danish Prime Minister Mette Frederiksen told Danish TV on Tuesday that "Greenland belongs to the Greenlanders" and that only the local population could determine its future.

However, she stressed Denmark needed close cooperation with the US, a Nato ally.

Greenland, which is the largest island in the world but has a population of just 57,000, has wide-ranging autonomy, although its economy is largely dependent on subsidies from Copenhagen and it remains part of the kingdom of Denmark.

It also has some of the largest deposits of rare earth minerals, which are crucial in the manufacture of batteries and high-tech devices.

Danish Broadcasting Corporation senior international correspondent Steffen Kretz, who has been reporting in Greenland's capital, Nuuk, said most of the people he had spoken to were "shocked" by Trump's suggestion he could use military force to take control of the territory.

While a majority of people in Greenland hoped for independence in the future, he said there was widespread acknowledgment that it needed a partner who could provide public services, defence and an economic foundation, as Denmark did now.

"I have yet to meet a person in Greenland who is dreaming of the island becoming a colony for another outside power like the USA."

Kretz told the BBC that while the Danish government had sought to "downplay" any confrontation with Trump, "behind the scenes I sense the awareness that this conflict has the potential to be the biggest international crisis for Denmark in modern history".

The president-elect's son, Donald Trump Jr, paid a brief visit to Greenland on Tuesday, in what he described as a "personal day trip" to talk to people.

He then posted a photo with a group of Greenlanders in a bar wearing pro-Trump caps.