"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."
Meanwhile, the Danish royal house also announced Thursday that King Frederik X would travel to Greenland on February 18 to show his "concern" for the island's inhabitants.
Trump's threats over Greenland plunged the transatlantic 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.
- 'Unfettered' access -
As part of the compromise with Washington, NATO members are expected to bolster their activities in the Arctic, while Denmark and Greenland could renegotiate a 1951 treaty on US troop deployments.
Louisiana governor Jeff Landry, who was named Trump's special envoy for Greenland in December said in an op-ed published in the New York Times that details were "being worked out".
"But the framework builds on the 1941 and 1951 defense agreements between the United States and Denmark and would enhance American, NATO and Greenlandic security and reaffirm longstanding trans-Atlantic defense obligations," Landry wrote.
"It would expand America's operational freedom, support new bases and infrastructure, facilitate deployment of advanced missile-defense systems like the Golden Dome and crowd out hostile Chinese and Russian influence," he explained.
At the same time, Landry stressed that "the reality is that no nation, or group of nations, is capable of securing Greenland without the United States."
Landry continued to add that Trump recognised the "uncomfortable fact" that "America must guarantee its own unfettered and uninterrupted access to key strategic territories in the Western Hemisphere, including both Greenland and the Panama Canal."
US Secretary of State Marco Rubio said Wednesday he expected a "good outcome" on Greenland as negotiations start.
Trump has repeatedly argued that the US needs the Arctic territory, home to some 57,000 inhabitants, for "national security".
In explaining his planned trip to Greenland, Denmark's King Frederik told reporters during a visit to Lithuania that "we feel very deeply for the Greenlandic people and we have been deeply affected by what has been happening in Greenland in recent weeks."
"We can sense from the media that the Greenlandic people have been very concerned. It is clear that this concerns us both," he added, referring to his wife, Queen Mary.
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