NATO chief Mark Rutte appeared to have pulled off a diplomatic coup by talking Trump down from his Greenland demands -- but swirling questions remained about their purported deal, and what might follow.

"We are back to a situation that seems much more acceptable, even if we remain vigilant," French President Emmanuel Macron said at the start of the emergency summit.

Trump's threats over the vast Arctic island -- an autonomous territory of NATO member Denmark -- plunged relations between Europe and its key ally Washington to a historic low.

While the immediate danger to NATO seemed to have passed, the bloc maintained an evening meeting called to address the crisis -- its focus now on how to handle the unpredictable US leader going forward.

Macron insisted that a push in the European Union to unleash its trade arsenal against the United States had helped persuade Trump to back down.

"We remain extremely vigilant and ready to use the instruments at our disposal if we were to face threats again," the French leader told reporters.

Denmark's Prime Minister Mette Frederiksen said support from across Europe for her country had been "extremely important in this very difficult situation".

"When we stand together and when we are clear and strong also in our willingness to stand up for ourselves, then the results will show," she said.

- Details scarce -

Trump backed down Wednesday night both on threatening to seize Greenland by force and on imposing tariffs against European allies, saying he had reached a "framework" of a deal on the island that satisfied him.

The startling turnaround came after talks at the Davos forum with Rutte, who told AFP afterwards that there was "still a lot of work to be done".

Details remain scant on any agreement, but a source familiar with the talks told AFP the United States and Denmark would renegotiate a 1951 defence pact on Greenland.

Trump said the accord would give Washington "everything we wanted" -- however, there was no sign he had succeeded in his repeated vow to make Greenland part of the United States.

Frederiksen said discussions about Denmark's sovereignty were off the table. "It cannot be changed," she said.

She told reporters in Brussels that Denmark was open to discussing the 1951 pact with the United States, "but it has to be in the framework of us as a sovereign state".

She also said NATO states backed having a "permanent presence" in the Arctic, including around Greenland.

Greenland's Prime Minister Jens-Frederik Nielsen said he did not know what had been agreed with Trump, but said he wanted to continue a "peaceful dialogue".

- 'Way to go' -

It was still unclear what exactly prompted Trump's U-turn.

German Chancellor Friedrich Merz welcomed Trump's retreat over Greenland, calling it "the right way to go". But speaking in Davos he also warned of perilous times ahead.

"We have entered a time of great power politics. The international order of the past three decades anchored in international law has always been imperfect. Today, its very foundations have been shaken," Merz said.

Europe has struggled to set red lines as its once-close American ally has turned hostile under Trump -- to the point of threatening its sovereignty.

"It's absolutely obvious for all of us that we have to do everything to protect our transatlantic relations," said Polish Prime Minister Donald Tusk.

"But what we need today in our politics is trust and respect among all partners, not domination, and for sure, not coercion."

The continent is ramping up defence spending to break its security reliance on the United States -- but for now, it still needs US help to end the Ukraine war, and deter the looming Russian threat to its east.

Greenland is only part of the picture, as the United States wages a broader attack on the EU's laws, politics and values -- points pressed home by Trump on the stage in Davos.

Leaders are well aware any respite may be short-lived, and indeed Trump was back with new threats Thursday afternoon, vowing reprisals if European countries dumped US Treasury bonds to pressure Washington.