Trump’s controversial remarks came hours after he announced his intention to nominate Ken Howery, his former ambassador to Sweden, to be the new ambassador to Denmark.
Mr Howery said he was “deeply humbled” by the nomination and looked forward to working with staff at the US Embassy in Copenhagen and the US Consulate in Greenland to “deepen the ties between our countries”.
Trump’s initial proposal in 2019 for the US to buy Greenland, the world’s largest island, drew a similarly sharp rebuke from leaders.
Then-Denmark Prime Minister Mette Frederiksen, who still holds the role, called the idea “absurd,” leading Trump to cancel a state trip to the country.
He is not the first US president to offer to buy Greenland. The idea was first floated in the 1860s during the presidency of Andrew Johnson.
Separately, on Sunday, Donald Trump threatened to regain control of the Panama Canalone of the world’s most important waterways – accusing Panama of charging exorbitant fees to access it.
The president of Panama later declared that “every square meter” of the canal and the surrounding area belonged to his country.