Denmark's foreign minister said he was "more optimistic" after technical talks kicked off with the United States over Greenland.

Lars Lokke Rasmussen told journalists at an EU meeting in Brussels that they had the "very first meeting at senior official level in Washington yesterday regarding the Greenlandic issue."

"It went well in a very constructive atmosphere and tone, and new meetings are planned. It's not that things are solved, but it's good," he said.

The trilateral talks come after U.S. President Donald Trump last week backed down from his threats to seize the autonomous Arctic territory of Denmark, a member of the EU and NATO.

"There was a major detour. Things were escalating, but now we are back on track," Rasmussen said.

"I'm slightly more optimistic today than a week ago."

Trump's threats over Greenland plunged the transatlantic alliance into its deepest crisis in years.

The unpredictable U.S. leader backed off his desire to take control of Greenland after saying he had struck a "framework" deal with NATO chief Mark Rutte to ensure greater American influence.

But few concrete details appear to have been agreed upon, with the authorities in Denmark and Greenland refusing to discuss handing over sovereignty.

"I have stated on many occasions, we, of course, share the U.S. security concerns regarding the Arctic; this is something we want to solve in close cooperation," Rasmussen said.

As part of the compromise with Washington, NATO is expected to bolster its activities in the Arctic, while Denmark and Greenland could renegotiate a 1951 treaty on U.S. troop deployments.