US Secretary of State Marco Rubio has announced he will hold talks with Denmark next week amid concerns over America's desire to acquire the Danish territory of Greenland.

Marco Rubio's statement to reporters following a closed-door briefing with US senators comes a day after the White House said US President Donald Trump had been discussing options including military force to acquire Greenland.

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.

The Trump administration claims Greenland is vital to US security. Denmark warned that any attack would jeopardize NATO's military alliance.

If the president identifies a threat to the national security of the United States, every president retains the option to address it through military means, Rubio stated.

Earlier, French Foreign Minister Jean-Noël Barrot relayed that Rubio had ruled out the possibility of an invasion of Greenland in a phone call.

European leaders, rallying behind Denmark, stated: Greenland belongs to its people, and only Denmark and Greenland can decide on matters concerning their relations. They stressed the need for NATO allies to collectively ensure Arctic security.

Reacting to the tensions, Morgan Angaju, an Inuit resident in Greenland, expressed fear about being treated as a territory to claim rather than as a people with their own rights.