“Any attempt to interfere in the internal affairs of the Kingdom will, of course, be unacceptable.”
Frederiksen said at a press conference that the government was looking “very seriously” at the matter.
The White House is yet to comment, but the US State Department sought to distance itself from the reports.
“The US Government does not control or direct the actions of private citizens,” the department said in a statement late on Wednesday, Washington time.
“The President, the Vice President, and the Secretary of State have all been clear: the United States respects the right of the people of Greenland to determine their own future.”
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The Danish Broadcasting Corporation, known as DR, reported on Wednesday that several Danish government sources confirmed that at least three American men with ties to the US president and the White House had been active in Greenland in a covert operation.
One of the reporters, Niels Fastrup, told British podcast The News Agents that the goal was to break Greenland free of Denmark to enable a US takeover.
“What our sources described to us is a pattern of travel activity where you would have these US individuals going between the US and Greenland,” he said.
“And when in Greenland, they would work in a clandestine fashion to try to set up what you could describe as a Greenlandic liberation movement.
“The tasks being done, according to our sources, involve things like working out lists of Greenlanders sympathetic towards Donald Trump’s plans for taking over Greenland.
US President Donald Trump and Denmark Prime Minister Mette Frederiksen.Credit: AP
“It also involves the opposite: trying to identify people against this.”
Fastrup said the operation also sought to create stories that could increase division between Denmark and Greenland, but he was cautious not to say whether or not this was directed by the White House.
“We are not at present able to establish whether they are working on their own or on behalf of Donald Trump directly,” he said on the podcast.
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Greenland has a population of 58,000 and is an autonomous territory within the Kingdom of Denmark, but it has chafed at the control exerted by Copenhagen.
In one example of that tension, Frederiksen issued a formal apology on Wednesday for a Danish government program from the 1960s to the early 1990s that forced around 4500 Inuit women to wear a contraceptive coil, or intrauterine device (IUD), without their consent.
“We cannot change what has happened. But we can take responsibility. Therefore, on behalf of Denmark, I would like to say: I am sorry,” she said in a statement reported by Agence France-Presse.
Even so, polling company Verian found very little support for Trump’s proposal when it asked Greenlanders in January if they wanted to leave Denmark and become part of the US.
“The results show that 85 per cent of Greenlanders do not want to leave the realm and become part of the United States, while 6 per cent want to leave the Danish realm and become part of the United States, whereas the remaining 9 per cent are undecided,” it said. The survey was based on questions to 497 respondents.
Trump’s son, Donald Jr, visited Greenland in January in an aircraft carrying the Trump brand, to be greeted by a small group of supporters.
“Greenland is an incredible place, and the people will benefit tremendously if, and when, it becomes part of our Nation,” Trump said on social media ahead of that visit.
“We will protect it, and cherish it, from a very vicious outside World.”
The Danish monarch, King Frederik, has responded to interest from the US by changing the royal coat of arms to give a greater prominence to Greenland.
The US does not currently have an ambassador in Denmark as Trump’s nomination – PayPal co-founder Kenneth Howery – is still pending.
When Howery was announced in December as the US president’s pick for ambassador, Trump posted on social media that “ownership and control of Greenland is an absolute necessity”.
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