"We've done no planning yet. We have not received political guidance to move out," US General Alexus Grynkewich, NATO's supreme commander for Europe, said after a meeting of alliance top brass.

"We're doing some thinking about how we would organise for it -- no planning has started yet, but we're ready."

Launching a NATO mission in the Arctic has been floated as a possible solution after Trump used the perceived threat from Russia and China to justify his desire to take Greenland.

Trump climbed down from his threats against the territory after claiming a deal had been struck in talks with NATO chief Mark Rutte in Davos Wednesday.

Details remain scant on exactly what, if anything, has been agreed -- but NATO said part of the plan was for the alliance to look at boosting security in the Arctic.

Grynkewich said no NATO exercises were planned on Greenland in the near future, but that the alliance would hold long-scheduled drills elsewhere in the Arctic.

He played down concerns that Trump's threats against Greenland -- an autonomous territory of Denmark, a fellow NATO member -- had damaged the 32-nation alliance.

"We remain strong, we remain united, and we remain ready," Grynkewich said.