Danish Prime Minister Mette Frederiksen said on Thursday that Denmark and Greenland remain open to constructive dialogue on Arctic security provided discussions respect her country's territorial integrity.

U.S. President Donald Trump on Wednesday walked back threats to impose tariffs on European countries opposing his desire to seize Greenland in remarks at Davos, and ruled out the use of force. He suggested progress had been made on a deal to end the dispute over the semi-autonomous Danish territory.

After meeting with NATO Secretary General Mark Rutte, Trump said Western Arctic allies could forge an agreement that satisfies his desire for a "Golden Dome" missile‑defence system to protect the U.S. and access to minerals, while blocking what Trump says are Russia and China's ambitions. Both countries have rejected the claim.

Arctic security a matter for all of NATO

Frederiksen said NATO was fully aware of Denmark's position, and that she had been informed that Rutte's talks did not involve her country's sovereignty.

"Security in the Arctic is a matter for the entire NATO alliance. Therefore, it is good and natural that it is also discussed between NATO's secretary general and the president of the United States," Frederiksen said in a statement.

"The Kingdom of Denmark wishes to continue to engage in a constructive dialogue with allies on how we can strengthen security in the Arctic, including the United States' Golden Dome, provided that this is done with respect for our territorial integrity," she said.

U.S. military scaled down Greenland presence

The U.S. had thousands of troops on Greenland during the Cold War, but in recent decades has radically scaled back its military presence on the resource-rich island, which is part of NATO through Denmark's membership in the alliance.

The U.S. military maintains a permanent presence at the Pituffik air base in northwest Greenland under a 1951 agreement that also allows the U.S. to build bases provided it notifies Denmark and Greenland.

The island has extensive autonomy from Denmark, though this excludes foreign affairs and defence unless agreed. Since 2009, it has had the right to declare independence after holding a referendum and gaining Danish parliamentary approval.

"... it is of course only Denmark and Greenland itself that can strike agreements regarding questions concerning Denmark and Greenland," Frederiksen said.

Aaja Chemnitz, a Greenlandic member of the Danish parliament, said nothing could be decided without the participation of Greenland.

"NATO in no way has a sole mandate to negotiate anything without us from Greenland," she said.