Thousands of protesters gathered across Denmark on Saturday in solidarity with Greenland amid US President Donald Trump’s threat to annex the Arctic island, demanding that the United States respect Greenlanders’ right to self-determination.

Trump says Greenland is vital to US security because of its strategic location and large supply of minerals and has not ruled out the use of force to take it. European nations this week sent military personnel to the island at Denmark's request.

Chanting “Greenland is not for sale” and holding banners with slogans such as “Hands off Greenland” alongside Greenland’s red and white “Erfalasorput” flag, demonstrators assembled in Copenhagen’s City Hall Square before marching towards the US embassy.

"I am very grateful for the huge support we as Greenlanders receive ... we are also sending a message to the world that you all must wake up," said Julie Rademacher, chair of Uagut, an organization for Greenlanders in Denmark.

"Greenland and the Greenlanders have involuntarily become the front in the fight for democracy and human rights," she added.

Reuters video footage showed thousands of protesters. Spokespersons for organisers and police declined to provide a crowd estimate.

Protests were also ongoing in other locations across Denmark and are scheduled to take place in Nuuk, Greenland's capital, later on Saturday.

Trump's repeated statements about the island have triggered an unprecedented diplomatic crisis between the United States and Denmark, both founding members of the NATO military alliance, and have been widely condemned in Europe.

The Greenland territory of 57,000 people, governed for centuries from Copenhagen, has carved out significant autonomy since 1979 but remains part of the Kingdom of Denmark which controls defence and foreign policy, and funds much of its administration.

All five political parties elected to Greenland's parliament ultimately favour independence, but they disagree on the timeline of such a move and have in recent days said they would rather remain part of Denmark than join the United States.

The protests in Denmark were organised by Greenlandic groups in cooperation with ActionAid Denmark, an NGO.

"We demand respect for the Danish Realm and for Greenland's right to self-determination," said Camilla Siezing, chair of Inuit, the Joint Association of Greenlandic Local Associations in Denmark.

Some 17,000 Greenlanders live in Denmark, according to Danish authorities.

Just 17% of Americans approve of President Donald Trump's efforts to acquire Greenland, and large majorities of Democrats and Republicans oppose using military force to annex the island, a found. Trump "fake".