The meeting came after a particularly turbulent period for the transatlantic alliance. The disagreement over Greenland has further undermined Western unity and cast yet more doubt on the trustworthiness and dependability of the current incumbent of the White House.

If there was even a hint of Trump being capable of self-reflection, one could add that it was a rather embarrassing week for him, on at least three counts.

First, Trump seemed to perform a climb-down in his speech at the World Economic Forum in Davos on 21 January when he ruled out the use of force to acquire Greenland for the US. He also dropped the threat of imposing tariffs on European NATO members which had dispatched military personnel to Greenland in a highly symbolic show of support.

Second, he insisted that the US would always be there for its NATO allies, in contrast to earlier pronouncements that the American security guarantee for Europe was conditional on their financial contributions to NATO. But, as is usually the case with Trump, it was one step forward, two steps back, as he went on to cast doubt on the allies reciprocating in an American hour of need.

Worse still, in a subsequent interview with Fox News, he denigrated the sacrifices of allied servicemen and women in Afghanistan, prompting a chorus of justified outrage from across the alliance.

After a phone call with the British Prime Minister Keir Starmer on Saturday and an expression of concern in a message conveyed “through backchannels” from King Charles III, Trump changed his tune. He did not exactly apologise, but he used his Truth Social platform to praise the bravery and sacrifices of British soldiers in Afghanistan. No other NATO ally has received even that acknowledgement yet.

Third, by the end of the week we were also reminded that progress on one of Trump’s flagship projects — making peace between Russia and Ukraine — is as elusive as ever. The US president appeared to have had a constructive meeting with Zelensky in Davos. But the much-touted agreement on US security guarantees has not yet been officially signed, and there’s been no progress on a deal for Ukraine’s post-war reconstruction either.

Contrary to how swiftly the US president threatened the imposition of tariffs on supposed allies for sending a few dozen soldiers to Greenland, Trump failed — yet again — to get tough on Putin. There is still no sign of a vote on a bipartisan Russia sanctions bill which Trump allegedly greenlit in early January.

The bill, in the making since the spring, aims to undermine Russia’s ability to finance its war against Ukraine and “to provide sustainable levels of security assistance to Ukraine to provide a credible defensive and deterrent capability”.

One could, therefore, argue that it was a bad week for Trump and a much better week for the rest of the Western alliance. After all, NATO is still intact. Europe seems to have discovered more of a backbone. Perhaps more importantly, they are realising that pushing back against Trump is not futile.

The US president has neither abandoned Zelensky nor walked away from mediating between Russia and Ukraine. And Trump might soon get distracted by plans for regime change in Cuba or Iran, preventing him from wreaking any more havoc in Europe.

But such a view underestimates both the damage already done to relations between Europe and the US and the potential for things to get worse. Consider the issue of Greenland. Trump’s concession to renounce the use of force was, at best, only a partial climb-down. Throughout his speech, Trump reiterated several times that he still wants “right, title and ownership” of Greenland.

As it’s not at all clear what his framework deal actually entails, his closing comments on Greenland included an unambiguous warning to other NATO members that they can “say ‘yes’ and we will be very appreciative, or … ‘no’ and we will remember”.

There is already, it seems, some advance remembering happening in Trump’s renamed Department of War, which released its new national defence strategy on Friday night. According to the document, the Pentagon will provide Trump “with credible options to guarantee US military and commercial access to key terrain from the Arctic to South America, especially Greenland, the Gulf of America, and the Panama Canal”.

On NATO, Trump’s ambivalence towards the alliance goes deeper than his most recent comments. Critically, it is the casual nature with which Trump treats this core pillar of international security that has fundamentally undermined the trustworthiness of the US as a dependable partner.

Combined with the efforts to set up his Board of Peace as an alternative to the UN, there can be little doubt left that the US president has his sights trained on the very institutions that Washington spent decades building.

When it comes to Ukraine, meanwhile, Trump may well just be dangling the prospect of an agreement to try to get Zelensky to make territorial concessions that will please Putin. If past encounters are any guideline, Putin will accept the concessions but baulk at the prospect of the US, or anyone, offering Kyiv security guarantees.

Trump, going on what we have seen over the past year, is then likely to water down what he apparently agreed in order not to jeopardise a deal with Putin. I think it most likely that Zelensky and Ukraine will, yet again, be left out in the cold.

For Trump, ending the war seems increasingly to be a way to enable future business deals with Russia, even it means sacrificing 20% of Ukrainian territory and the long-term security of his European allies in the process.

The conclusion to draw for European capitals from London to Kyiv from a week of high drama should not be that Trump and the relationship with the US can be managed with a new approach that adds a dose of pushback to the usual flattery and supplication.

After one year of Trump 2.0, America-first has become America-only. Europe and its few scattered allies elsewhere need to start acting as if they were alone in a hostile world. Because they are.