"I think the desire from the US president is exactly the same. He is very serious about this theme," Frederiksen said at a panel of the Munich Security Conference, Xinhua reported.
"We have to protect sovereign states. We have to protect people's right to self-determination. And the Greenlandic people have been very clear: they don't want to become Americans," she stressed.
According to media reports, a US-Denmark-Greenland working group has been established to address US "security concerns" in the Arctic.
"We now have a working group, it's good. We will try to see if we can find a solution ... But of course, there are red lines that will not be crossed. And we will stick to our strategy," Frederiksen said on another occasion on Friday.
Concerns about a possible US armed seizure of Greenland have eased as Trump ruled out taking Greenland by military force in talks in the Swiss Alpine town of Davos last month.
Meanwhile, Trump also announced his decision not to follow through on his threat to impose new tariffs on eight European countries over Greenland following a meeting with NATO Secretary General Mark Rutte.
Greenland, the world's largest island, is a self-governing territory within the Kingdom of Denmark, with Copenhagen retaining control over defense and foreign policies. Since returning to office in 2025, Trump has repeatedly expressed a desire to "obtain" Greenland, a move that has sparked backlash across Europe.