The European Commission president has called Donald Trump’s planned new tariffs an error and questioned how far he can be trusted, as the US president said there was “no going back” on his goal to control Greenland.

Ursula von der Leyen said at the World Economic Forum in Davos, Switzerland, on Tuesday that Trump’s threat to impose a 10% tariff on imports from eight European countries that oppose a US takeover of the Arctic island was “a mistake, especially between longstanding allies”.

Appearing to call Trump’s trustworthiness into question, von der Leyen said the EU and US had “agreed to a trade deal last July, and in politics, as in business, a deal is a deal. When friends shake hands, it must mean something.”

Europeans, she added, “consider the people of the US not just our allies, but our friends”. She warned against plunging relations into a downward spiral but said the EU’s response, if necessary, would be “unflinching, united and proportional”.

Trump has ramped up his push to grab Greenland, a largely self-governing part of the Danish kingdom, in recent weeks, saying the US would take control of the vast Arctic island “one way or the other” and: “Now it is time, and it will be done!!!”

On Saturday he threatened to impose from 1 February a punitive 10% tariff, increasing later to 25%, on imports from Denmark, Norway, Sweden, France, Germany, the UK, the Netherlands and Finland unless they dropped their objections to his plan.

After speaking to the Nato secretary general, Mark Rutte, the US president posted on social media on Tuesday that he had “expressed to everyone, very plainly, Greenland is imperative for National and World Security. There can be no going back.”

He posted an AI image of himself, the US vice-president, JD Vance, and the secretary of state, Marco Rubio, planting a US flag next to a sign reading: “Greenland, US territory est 2026.” Another image showed a map with Canada and Greenland as part of the US.

Separately, Trump posted a message to him from the French president, Emmanuel Macron, who said he did “not understand what you are doing on Greenland”. The US president had earlier threatened to hit French wine and champagne with a 200% tariff.

The escalating row has plunged trade relations between the EU and the US into fresh chaos, forcing the bloc to consider retaliatory measures, and also risks unravelling the Nato transatlantic alliance that has guaranteed western security for decades.

Trump is due to attend the WEF gathering later this week to meet EU leaders who are mulling retaliatory measures that could include a package of tariffs on €93bn (£80bn) of US imports that has been suspended for six months.

Another option is the bloc’s “anti-coercion instrument” (ACI), which has never been used but would limit US access to public tenders, investments or banking activities and restrict trade in services, including digital services.

“This is not a question about the Kingdom of Denmark, it is about the entire transatlantic relationship,” Denmark’s economy minister, Stephanie Lose, said in Brussels. “At this point in time, we do not believe that anything should be ruled out.”

However, the US treasury secretary, Scott Bessent, said on the sidelines of the Davos gathering that US relations with Europe were strong and urged partners to “take a deep breath” and let tensions over Greenland “play out”.

Bessent said a solution would be found and European “hysteria” was unjustified. “It’s been 48 hours. Sit back, relax,” he said. “I am confident the leaders will not escalate and that this will work out in a manner that ends up in a very good place for all.”

Trump has rocked the EU and Nato by refusing to rule out using military force to seize Greenland, a strategically important, mineral-rich island that is covered by many of the protections offered by the two organisations since Denmark is a member of both.

He has repeatedly said the US needs to take control of the territory for “national security”, despite the US already having a military base on the island and a bilateral agreement with Denmark allowing it to massively expand its presence there.

Von der Leyen said in her speech that the EU was working on a package for Arctic security based on Greenlandic and Danish sovereignty, a big investment surge in Greenland, and cooperation with the US in the region.

The Danish public broadcaster TV2 reported that 58 Danish troops had landed in Greenland on Tuesday to join about 60 others who were dispatched earlier for a multinational military exercise, Operation Arctic Endurance.

European leaders are considering establishing a more permanent military presence in the high north to help guarantee security in the Arctic region, a key US demand, the Swedish defence minister, Pål Jonson, said.

Jonson said that European members of Nato were “doing what’s called a reconnaissance tour in order to identify what kind of needs there are when it comes to infrastructure and exercises and so forth”.