Trump backed down on 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.

Details of the agreement made at the World Economic Forum in the Swiss ski resort of 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 said earlier in a statement.

The United States and Denmark will renegotiate a 1951 defence pact on Greenland, a source familiar with the talks between Trump and Rutte told AFP on Thursday.

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

Danish Defence 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."