Officials from Greenland have repeated that the Danish territory will never be for sale during talks over the future of the Arctic island with the special envoy of United States President Donald Trump.

Jeff Landry, who Trump appointed late last year to pursue control of the island, arrived in Greenland's capital Nuuk on Sunday and met with Greenland's Prime Minister Jens-Frederik Nielsen and Foreign Minister Mute Egede on Monday.

Speaking at a news conference after the meeting, Nielsen described initial talks with Landry as "constructive", but noted that there was no sign the US stance toward Greenland had altered.

He said he emphasized to Landry that the giant island, coveted by the US because of what Trump says are national security concerns and amid reports the US wants access to its minerals, will never be for sale.

The territory's premier said: "We clearly reiterated that the people of Greenland are not for sale and that Greenlanders have the right to self-determination. This is not a subject for negotiation. We believe there is progress, and from Greenland's side we are focused on finding a solution that is good for us all, and most importantly that threats of annexation, takeover, or a purchase of Greenland and the Greenlandic people do not occur."

Egede said Washington has not abandoned its goal of acquiring the territory.

"We have our red line. The Americans' starting point has not changed either," he said.

Landry, who was slated to attend an economic forum in Nuuk on Tuesday and Wednesday, did not give a statement after the talks, but had told local media on Sunday he was there to "listen and learn".

Speaking to Danish broadcaster TV 2, Landry said he was in Greenland to look for ways to deepen ties with the US. He added that Trump had told him to "go over there and make a bunch of new friends".

Tensions between the US and Denmark, both founding members of NATO, erupted into a diplomatic crisis late last year over Trump's push to acquire the island, which is a goal the president first expressed in 2019.

Since then, to ease tension, Greenland, Denmark, and the US have agreed to hold high-level diplomatic negotiations, and a working group was established to discuss the US position.

The BBC reported last week that the US is seeking to expand its military presence in Greenland, with talks progressing in recent months.

US officials want to open three new bases in the south of the island, which would be formally designated as US sovereign territory, the report said.

Denmark has previously expressed a willingness to discuss additional US military bases on the island.

The Daily Telegraph newspaper reported this week that US diplomats are also seeking veto authority over large foreign investments in Greenland, to shut out strategic rivals.