There, he bluntly accused 23 out of 28 Nato countries of taking advantage of US taxpayers by failing to pay their way in the Atlantic alliance.

In talks with EU leaders, Trump appeared to display a limited grasp of how the world’s biggest market operates a common trade policy, railing against Germany’s “bad, very bad” surplus with his country.

Rolled eyeballs were the order of the day among senior EU aides who couldn’t decide whether Trump was badly briefed, incapable of mastering a complex brief or consciously engaging in megaphone diplomacy in order to show he is serious about his “America first” agenda.

Brussels also provided one of the abiding images of the trip when the leader of the free world was filmed muscling Montenegrin Prime Minister Dusko Markovic out of his way to get to the front of a photo opportunity.

European hopes Trump could be pressured into a more conciliatory stance on trade, climate change and migration at the G7 summit in Sicily were also dashed.

It left his Italian hosts with virtually nothing to show after months of preparations. Compounding the diplomatic damage, Trump upstaged Prime Minister Paolo Gentiloni’s closing press conference by tweeting that he would next week make his long-anticipated decision on US observance – or not – of the Paris climate accords.

Julianne Smith, from the Centre for a New American Security, said the summit showed how team Trump appeared determined to maintain a “strategic ambiguity” whatever the cost to long-established relationships.

Watch: Trump lauds trip abroad as challenges await

“We understand that this is a tool that the administration finds useful to deal with adversaries,” she said. “But for European allies across the continent, it’s creating a tremendous amount of uncertainty and insecurity.”

Another US foreign policy expert, Derek Chollet, said it was no coincidence that the mood of the trip changed dramatically when Trump left the controlled confines of the Middle East.

“In Europe, where the leaders were less fawning and the press less forgiving, Trump got himself into trouble,” he wrote in Foreign Policy. “The contrast was remarkable: for this first time I can think of, we saw an American president who is more at home among Arab monarchs than democratic European allies.”

With the exception of Japan’s Shinzo Abe, with whom he shares a love of golf, Trump appears to have found little rapport with other G7 leaders.

His stonewalling on climate change amounted to politically damaging rebuffs for new French president Emmanuel Macron and Angela Merkel.

The German chancellor made no secret of her irritation, describing the discussion with Trump on the issue as “difficult and unsatisfactory”. Macron was more diplomatic, claiming to see signs of progress and describing Trump as “pragmatic and ready to work”.

Canadian Prime Minister Justin Trudeau also opted to see the glass half-full, saying: “I can assure you President Trump was in listening mode.”

Several summit participants suggested the US team appears still to be a prisoner of the dynamics of last year’s election campaign.

That, they said, explained the confrontational rhetoric despite the administration having yet to define exactly what it plans to do on the key issues of trade and climate change.

Not that Trump himself admitted to any confrontation. In his departure speech he claimed the summit had “made great progress toward very, very vital goals”.

“I laid out my vision for economic growth and fair trade,” he said. “And I called for much greater security and cooperation on matters of both terrorism, immigration, migration, to protect our citizens. From Saudi Arabia, to Israel, to Nato, to the G7, we made extraordinary gains.”