Over the course of a week, he had a bruising telephone call with the leader of Australia , one of America's closet allies. He complained to the Mexican President about that country's "handling" of "tough hombres."

Trump on Friday warned in a tweet that Iran was "playing with fire" with its ballistic missile tests, part of an emerging strategy designed to show his administration will take a much harder line with the Islamic Republic.

But his administration stuck to the tools of traditional diplomacy by using a statement from Trump's press secretary Sean Spicer to warn Israel that new Israeli settlement activity could potentially hamper the peace process, a new stance for a White House that's remained adamant in its support for Prime Minister Benjamin Netanyahu.

Throughout his campaign, Trump hailed the virtues of being unpredictable on the world stage. Much to the happiness of some of his supporters, he's following through. But in the process, Trump is confusing much of the world. He's also handing some leaders, such as those in the United Kingdom and Mexico, political headaches of their own after encountering Trump. And some of America's allies are beginning to warn that Trump is putting over 70 years of transatlantic cooperation at risk.

"His style of diplomacy is very different from his recent predecessors," former Australian Prime Minister Kevin Rudd told CNN International's Hala Gorani Thursday. "He is much more in your face. I suppose the diplomacy of the rest of us is kind of going to have to get used to that."

Michael Fullilove, the executive director of the Lowy Institute, a top Australian think-tank, said that while the US-Australia alliance would remain strong in the aftermath of the tense phone call, Trump's approach would inevitably have an impact.

"It's a level of discourtesy that we don't expect," he said. "It will continue to inform the Australian public's view of Mr. Trump. I think inevitably it would inform public opinion about the alliance."

Transactional diplomacy

Trump seems to view diplomacy through the prism of a business transaction, where there are winners and losers and a belief that even allies can take advantage of the US.

His foreign policy thinking -- at least so far -- appears to be focusing more on the mechanics of individual national relationships and less on a strategic vision in which allies are a vehicle for expressing US power and influence around the globe.

The President's phone call with Australian Prime Minister Malcom Turnbull went off the rails when discussion turned to a deal concluded by former President Barack Obama to allow 1,250 refugees from an offshore detention center to come to the United States.

Trump tweeted Thursday that the deal was "dumb," even though Spicer has said the US would honor the agreement and despite the President's order to temporarily halt all refugees from entering the country.

The President was still fulminating about the deal by Thursday afternoon.

"I just said why?... Why are we doing this? What's the purpose?" Trump told reporters. "We have wonderful allies and we're going to keep it that way but we need to be treated fairly also."

Trump's decision to question the deal has rattled relations with Australia, a crucial pillar of US Asia-Pacific strategy, a member of the Five Eyes intelligence sharing agreement and an ally that has battled alongside the United States dating back to World War I.

Sen. John McCain, who fought with Australians in Vietnam, took it upon himself to smooth over relations on Thursday following Trump's showdown with Turnbull, telephoning Australia's ambassador to Washington.

"This in my view was unnecessary and frankly, harmful," the Arizona Republican said, adding that the dispute was far less important than cooperation, including joint training missions involving US Marines in the northern Australian city of Darwin.

Senior Democrats were also disturbed by the argument.

Virginia Sen. Tim Kaine said to have a "contentious conversation and name call (a) country or the Prime Minister of a country that is one of our greatest allies in Asia is foolish."

"He is doing kind of amateur hour stuff on matters of significant national importance," said Kaine, who was the 2016 Democratic vice presidential nominee.

Lesson for foreign leaders

Foreign policy experts said the US-Australia relationship remains too strong to be damaged. But the spat will be seen by other foreign leaders as a lesson in the difficulty of dealing with Trump.

British Prime Minister Theresa May found out that leaders who align themselves with Trump can get burned. The President didn't tell her he was signing an executive order restricting travel from seven predominantly Muslim countries soon after she left the White House last Friday, exposing her to a torrent of political criticism back home.

Trump's frequent criticisms of the European Union, which he has branded corrupt while apparently rooting for more nations to join Britain by voting to leave, is irking US allies, who see the block, for all its faults, as the root of decades of peace in Europe, a continent previously wracked by centuries of war.

"It is unacceptable that there should be, through a number of statements by the US President, pressure on what Europe should be or what it should no longer be," French President Francois Hollande said at the EU summit in Malta on Friday,

"There is no future with Trump if it's not worked together," Hollande said, according to an official Twitter account for France's representative to the EU.

Trump has also criticized the other bulwark of European security, NATO, as obsolete and has far more in common with populist leaders seeking to make an impact in elections this year in the Netherlands, France and Germany than the ruling elites in those nations.

Despite anodyne government readouts, there were also hints of tension in Trump's weekend call with German Chancellor Angela Merkel, whom the President has criticized for welcoming Syrian refugees.

Her office said Merkel "explained" to Trump that the Geneva Conventions require nations to offer a haven from refugees fleeing war.

But Trump is unapologetic about the bracing conversations he is having with world leaders -- a sign the White House is more concerned about Trump projecting a strong image on the world stage than stepping on diplomatic toes.

"The world is in trouble, but we're going to straighten it out. OK? That's what I do. I fix things. We're going to straighten it out," Trump said at the National Prayer Breakfast on Thursday. "Believe me. When you hear about the tough phone calls I'm having, don't worry about it. Just don't worry about it. They're tough. We have to tough ... We're taken advantage of by every nation in the world virtually. It's not going to happen anymore."

Trump's pugnacious approach to diplomacy is not surprising given his personality, which he used to great effect in his business career. While his attitude dismays foreign policy elites, it's likely to be welcomed by voters who turned to him in search of strong leadership and see his encounters as a manifestation of his "America First" philosophy.

But several diplomats have said Trump's acute course corrections in foreign policy and blunt manner make it difficult to decipher exactly where the United States now stands on key global issues.

Private vs. public arguments

Getting tough with America's friends also represents a break from previous administrations where disagreements often erupted but were not litigated in public. The White House may find in future that creating political problems for friendly leaders will make it more difficult for them to compromise with Washington or even to send troops to help fight America's wars.

"We have an unwritten rule in diplomacy, you are going to argue with your friends but do it behind closed doors, don't expose differences, in public," Nicholas Burns, a longtime US diplomat and former under secretary of state for political affairs, told CNN International. "Don't make life difficult for your friends, the Prime Minister of Australia, the Chancellor of Germany, the President of Mexico."