Davos, Switzerland - Denmark said NATO chief Mark Rutte cannot negotiate on its behalf over Greenland, a day after US President Donald Trump announced a vague deal for the Arctic island's future.

Trump softened his threats to seize Greenland by force after meeting Rutte on Wednesday, saying he had reached a "framework" of a deal on the Danish autonomous territory.

But details of the agreement made at the World Economic Forum in Davos remain scant.

"The position of Denmark and that of Greenland are the same, and no negotiations were held yesterday with NATO about our sovereignty," Denmark's Prime Minister Mette Frederiksen told Danish television.

"Of course it is only Denmark and Greenland themselves that can make decisions on issues concerning Denmark and Greenland," she insisted in an earlier in a statement.

A source familiar with the talks between Trump and Rutte told AFP on Thursday the US and Denmark would renegotiate a 1951 defense pact on Greenland.

Putting US military bases on Greenland under US sovereignty had not been discussed during the talks, the source said.

Danish Defense Minister Troels Lund Poulsen said on social media Thursday that Rutte "cannot negotiate an agreement on behalf of Denmark or Greenland".

However, he said Rutte had "worked loyally to maintain unity within NATO" and it was "very positive" that the alliance wanted to do more to strengthen Arctic security.

"We have a clear red line," he added. "We will not cede sovereignty over parts of the kingdom."

Greenland's Deputy Prime Minister Mute Egede restated the message.

"Whatever pressure others may exert, our country will neither be given away, nor will our future be gambled with," he wrote on Facebook. "It is unacceptable to attempt to hand our land to others. This is our land – we are the ones who shape its future."