The United States is a strong ally of the European Union and the leading member of NATO and many in Europe were shocked by the suggestion that an incoming US leader could consider using force against an ally.
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Greenland's prime minister has said that the Arctic territory's people don't want to be Americans but that he understands US President-elect Donald Trump's interest in the island given its strategic location.
The comments from Múte B. Egede came after Trump said earlier this week that he wouldn't rule out using force or economic pressure in order to make Greenland, a semi-autonomous territory of Denmark, a part of the United States.
Trump said that it was a matter of national security for the US.
Egede acknowledged that Greenland is part of the North American continent and "a place that the Americans see as part of their world" but said he hadn't spoken to Trump since he made the comments.
Egede has been calling for independence for Greenland, casting Denmark as a colonial power that hasn't always treated the indigenous Inuit population well.
"Greenland is for the Greenlandic people. We do not want to be Danes, we do not want to be Americans. We want to be Greenlanders," he said at a news conference alongside Danish Prime Minister Mette Frederiksen in Copenhagen.
Trump's desire for Greenland has sparked anxiety in Denmark as well as across Europe.
The United States is a strong ally of the 27-nation European Union and the leading member of the NATO alliance and many in Europe were shocked by the suggestion that an incoming US leader could even consider using force against an ally.
But Frederiksen said that she sees a positive aspect in the discussion.
"The debate on Greenlandic independence and the latest announcements from the US show us the large interest in Greenland," she said.
"Greenland belongs to the Greenlanders – no one else."
Frederiksen and Egede spoke to journalists after a biannual assembly of Denmark and two territories of its kingdom, Greenland and the Faroe Islands.
The meeting had been previously scheduled and wasn't called in response to Trump's recent remarks.
Trump's eldest son also made a visit to Greenland on Tuesday, landing in a plane emblazoned with the word TRUMP and handing out Make America Great Again caps to locals.
The Danish public broadcaster, DR, reported on Friday that Trump's team encouraged homeless and socially disadvantaged people in Greenland to appear in a video wearing the MAGA hats after being offered a free meal in a restaurant.
The report quoted a local resident, Tom Amtof, who recognised some of those in a video broadcast by Trump's team.
"They are being bribed and it is deeply distasteful," he said.
Greenland has a population of 57,000. But it's a vast territory possessing natural resources that include oil, gas and rare earth elements, which are expected to become more accessible as ice melts because of climate change.
It also has a key strategic location in the Arctic, where Russia, China and others are seeking to expand their footprint.
Greenland, the world's largest island, lies closer to the North American mainland than to Denmark.
While Copenhagen is responsible for its foreign affairs and defence, the US also shares responsibility for Greenland's defence and operates an air force base there based on a 1951 treaty.