Demonstrators wore parody 'Make America Go Away' hats and chanted 'Greenland is not for sale', with large crowds gathering in Copenhagen and Nuuk.
Trump responded by announcing 10 per cent import tariffs on eight European countries that oppose his plans to take control of Greenland.
European nations deployed military personnel to Greenland at Denmark's request, while Greenland's parliament unanimously favours remaining part of Denmark.
Public opinion in the US largely opposes using military force to acquire Greenland, which is an autonomous country within the Kingdom of Denmark.