Taormina (Italy) (AFP) - Donald Trump's first trip overseas was supposed to be about building bridges and clarifying his administration's intentions to friends and foes alike.

Taormina (Italy) (AFP) - Donald Trump's first trip overseas was supposed to be about building bridges and clarifying his administration's intentions to friends and foes alike.

And the US president flew home Saturday boasting he had "scored a home run" everywhere he'd been, saying he had forged bonds with friends old and new in the fight against terrorism.

But behind him he left some of Washington's allies as bewildered as ever over his abrasive, unpredictable style and the substance of his policy plans.

Trip stops in Saudi Arabia and Israel and the Palestinian territories secured broadly favourable coverage with Trump seen by some commentators as having finally hit a presidential note.

He then emerged from his Vatican meeting with Pope Francis in buoyant spirits, declaring himself inspired to work harder than ever in pursuit of peace around the world.

But the mood started to sour when the 70-year-old hit Brussels on Thursday.

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.

Strategic ambiguity

U.S. President Donald Trump (R) speaks beside NATO Secretary General Jens Stoltenberg at the start of the NATO summit at their new headquarters in Brussels, Belgium, May 25, 2017. Reuters/Christine Hartmann

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 Montenegro's Prime Minister, Dusko Markovic, out of his way to get to the front of a photo opportunity.

And European hopes that Trump could be pressured into a more conciliatory stance on trade, climate change and migration at the G7 summit in Sicily were 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' 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 Center for a New American Security (CNAS), said the summit showed how team Trump appeared determined to maintain a "strategic ambiguity" whatever the cost to long-established relationships.

"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."

Stonewalling on climate

Residents of East Chicago, Ind., and supporters rally near a public-housing complex Wednesday, April 19, 2017, ahead of a visit by Environmental Protection Agency Administrator Scott Pruitt. Pruitt was scheduled to to tour the complex where roughly 1,000 people were ordered evacuated because of lead contamination. AP Photo/Teresa Crawford

Another US foreign policy expert, Derek Chollet, says 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.

"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," Chollet, a former Obama administration official, wrote in Foreign Policy.

With the exception of Japan's Shinzo Abe, with whom he shares a love of golf, Trump appears to have struck up 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. "I can assure you President Trump was in listening mode," he said.

- 'Extraordinary gains' -

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

That, they say, explains 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... 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," he said.