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

"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."

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

"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 transtatlantic alliance into its deepest crisis in years.

The unpredictable US 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 -- with authorities in Denmark and Greenland refusing to discuss handing over any sovereignty.

"I have stated on many occasions, we, of course, share the US 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 US troop deployments.