US President Donald Trump and his officials are 'actively' discussing a potential offer to buy the Danish territory of Greenland, the White House has confirmed.

It is 'something that's currently being actively discussed by the president and his national security team', White House spokeswoman Karoline Leavitt told reporters on Wednesday.

Both Greenland and Denmark have repeatedly stressed the island was not for sale.

Asked why the Trump administration had previously said it was not ruling out using military force to acquire Greenland, Leavitt replied that all options were always on the table but Trump's 'first option always has been diplomacy'.

Concerns over the future of the territory resurfaced after Trump's unilateral use of military force against Venezuela on Saturday to seize its President Nicolás Maduro. Denmark, a fellow NATO ally, says an attack on its territory would end the military alliance.

The Trump administration says Greenland is vital to US security.

Despite being the most sparsely populated territory, its location between North America and the Arctic makes it well placed for early warning systems in the event of missile attacks, and for monitoring vessels in the region.

In recent years, there has also been increased interest in Greenland's natural resources, including rare earth minerals, uranium, and iron, that are becoming easier to access as its ice melts due to climate change. Scientists think it could also have significant oil and gas reserves.

'The acquisition of Greenland by the United States is not a new idea,' Leavitt said. 'The president has been very open and clear with all of you and with the world, that he views it in the best interest of the United States to deter Russian and Chinese aggression in the Arctic region.'

Earlier in the day, French Foreign Minister Jean-Noël Barrot said Rubio had 'ruled out the possibility of an invasion' of Greenland in a phone call with him.

Meanwhile, European leaders issued a joint statement rallying behind Denmark, emphasizing that 'Greenland belongs to its people' and that only Denmark and Greenland can decide on their relations.

Among the residents of Greenland, reactions ranged from indifference to outrage, with some fearing a loss of autonomy and respect in the face of US ambitions.