"It's not only a crisis for NATO, it's a crisis for the transatlantic community at large, and a challenge to the world order as we have known it since World War Two," he said in an interview from the World Economic Forum in Davos.

"It is the future of NATO and the future of the world order that are at stake."

Rasmussen, a former Danish prime minister who led NATO from 2009 to 2014, urged the alliance's current head, Mark Rutte, and other European leaders to start taking a tougher line with the US president after he threatened tariffs.

"We have to change strategy and conclude that the only thing that Trump respects is force, strength and unity," Rasmussen said.

"That's exactly what Europe should demonstrate. The time for flattering is over. Enough is enough."

Rasmussen's comments came as European leaders -- including Rutte -- brace for meetings with Trump in Davos to try to talk him down.

Rasmussen insisted the current crisis swirling around NATO could still be "fixed" and the alliance could emerge stronger in the Arctic region.

But, he said, Trump's actions had already created a "mental break" between Washington and its long-time European allies which benefited Russia and China.

"This is a new situation that differs from all other disputes we have seen in the history of NATO," he said.

"If Trump would attack Greenland and take military action against Greenland, that would de facto mean the end of NATO."

- Distracting from Ukraine -

Rasmussen, 72, said that the Greenland issue had become a "weapon of mass distraction" for Trump that was drawing attention away from Russia's war in Ukraine.

"Everybody's now speaking about Greenland, which is not a real threat to North Atlantic security," he said.

"Russia's attack against Ukraine is the real threat, and attention should not be distracted from this real threat."

The former Danish premier, who led his country from 2001 to 2009, said that there needed to be a "constructive dialogue" now with the United States on Greenland.

He said Copenhagen and Washington could update their 1951 agreement governing troop deployments in Greenland, open the territory to US firms for mineral extraction and agree to keep Russia and China out.

But there could be no compromise on the fundamental question of ceding territory to Trump.

"We can accommodate all his wishes, except one," Rasmussen said.

"Greenland is not for sale and as a real estate expert he should know if an estate is not for sale you can't purchase it."