"Without us, right now you'd all be speaking German," President Donald Trump told his audience at the World Economic Forum in the Swiss Alps on Wednesday.

He may well have forgotten that German is the most widely spoken of the four official languages in Switzerland.

Many people – from Brussels to Berlin to Paris – will have found his speech to be insulting, overbearing and inaccurate.

In it, he presented the idea that Europe is careening down the wrong path. That is a theme Trump has frequently explored, but it has a different impact when delivered on European soil to the faces of supposed friends and allies.

There is undoubtedly great relief across Europe that the US president ruled out the use of military force to seize Greenland at the Davos forum.

But, even if he keeps his word, the fundamental problem remains that he wants a piece of land the owners say is not for sale.

Despite this, after the forum, Trump posted on social media that he was dropping his latest tariff threat against eight European countries he had ruled most guilty of thwarting his Arctic ambitions.

He claimed he had "formed the framework of a deal" for Greenland and the Arctic after a meeting with the Nato Secretary General Mark Rutte.

It is not clear how this plan would meet Trump's stated desire to own the island outright.

The proposed 10% taxes had been due to kick in from 1 February.

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"What is quite clear after this speech is that the president's ambition remains intact," Danish Foreign Minister Lars Løkke Rasmussen told reporters in Copenhagen - before Trump posted his climbdown.

He said Trump's comments about the military were "positive in isolation".

Thousands of miles from Davos, in Nuuk, the Greenlandic capital, government officials unveiled a new brochure offering advice to residents on what to do in the event of a "crisis" in the territory.

Self-Sufficiency Minister Peter Borg said the document was "an insurance policy". He said Greenland's government did not expect to have to use it.

Any hope in Europe that President Trump would take the sting out of this transatlantic crisis was smashed as he began to outline his uncompromising argument for taking the island.

He ignored the European insistence that Greenland is sovereign EU territory and framed its acquisition as a perfectly reasonable transaction given the military support the US had provided the continent for decades.

Trump insisted the US had been wrong to "give back" Greenland after securing it during World War Two.

Greenland has never been part of the United States.

Trump returned to his familiar refrain that the European members of Nato had done nothing for the US.

He disparaged Denmark in particular, recalling that in 1940 it "fell to Germany after just six hours of fighting and was totally unable to defend either itself or Greenland".

Trump's military history lesson failed to recall that the Danes were a key partner of the US-led invasion of Afghanistan and paid a heavy price.

Denmark lost 44 soldiers, proportionately more than any other ally apart from the US. They also lost personnel alongside US forces in Iraq.

Many other Nato allies supported the US after the 9/11 attacks in 2001.

It was French President Emmanuel Macron who was singled out for the most jibes.

He was mocked for his appearance in sunglasses on Tuesday - he had an eye problem - and his "tough" talking at the podium.

Trump insisted he liked Macron, before continuing: "Hard to believe, isn't it?"

But the whole joke is wearing thin for many European leaders.

They have spent a year trying to flatter, impress, and appease the US president, only to be presented with their biggest threat to date.

The European Union meets in Brussels on Thursday for an emergency summit, with top European politicians choosing their toughest language yet in response to US policy.

Trump stepping back from the tariff threat that had galvanised EU countries will take a large degree of tension out of the meeting.

But, they will want to know what exactly Trump and the Nato boss have concocted as a magic solution.

They may now decide there is no longer a need to ramp up the rhetoric around counter-tariffs and on rolling out the EU's "trade bazooka".

At the start of his one-hour and 12-minute meandering address, President Trump boasted that at home, "people are very happy with me".

After this latest extraordinary round of Trump democracy, it is a sentiment much harder to find in Europe, the president claims to love so much.