"It makes absolutely no sense to talk about the US needing to take over Greenland. The US has no right to annex any of the three countries in the Danish Kingdom," Danish Prime Minister Mette Frederiksen said in a statement on Sunday.
Trump told the magazine: "We do need Greenland, absolutely. We need it for defence."
He spoke a day after the US captured Venezuelan President Nicolas Maduro and the president said Washington would run the Latin American country, and this raised concerns in Denmark that the same could happen with Greenland, a Danish territory.
Frederiksen said: "I would therefore strongly urge the US stop the threats against a historically close ally and against another country and another people, who have very clearly said that they are not for sale."
The prime minister of Greenland, Jens-Frederik Nielsen, said in a statement, also on Sunday: "When the President of the United States says that 'we need Greenland' and links us to Venezuela and military intervention, it's not just wrong. It's disrespectful."
Trump on December 21 named Louisiana Governor Jeff Landry as special envoy to Greenland, drawing renewed criticism from Denmark and Greenland over Washington's interest in the mineral-rich Arctic island.
Trump has advocated for Greenland, a self-governing Danish territory, to become part of the United States. Landry publicly supports the idea.
The Arctic island's strategic position between Europe and North America makes it a key site for the US ballistic-missile defence system, while its mineral wealth is attractive as the US hopes to reduce its reliance on Chinese exports.
Greenland, a former Danish colony, has the right to declare independence under a 2009 agreement but depends heavily on Danish subsidies.
Denmark has sought to repair strained ties with Greenland over the past year, while also trying to ease tensions with the Trump administration by investing in Arctic defence.
