At the World Economic Forum in Davos, Switzerland, last January, President Trump insisted that his trademark "America First" policy “does not mean America alone.” But when Mr. Trump pulled the United States out of the Iran nuclear deal last week, reneging on an agreement negotiated and supported by close US allies, he displayed a bluntly unilateralist outlook that suggests he cares little whether or not the US is isolated. Whatever impact Trump's decision has on Iran and its nuclear program, it has sent a message to governments around the globe about Washington's willingness to live up to its word, even as presidents change. And observers generally say that message has not been well received. “It tells other countries … that the US can’t be trusted to keep its word from one administration to another,” says Makau Mutua, chairman of the Kenyan Human Rights Commission. “That is not how great powers conduct policy.” And while faith in the US recedes, China and Russia are nibbling at the edges of the US mantle of global leadership.

At the World Economic Forum in Davos, Switzerland, last January, President Trump insisted that his trademark America First policy “does not mean America alone.”

But when Mr. Trump pulled the United States out of the Iran nuclear deal last week, he ignored and antagonized Washington’s oldest and closest allies; he reneged on an international agreement enshrined in a United Nations resolution; and he displayed a bluntly unilateralist outlook that suggested he cares little whether or not the US is isolated.

That left friends and foes alike around the world scrambling to figure out the shape of the new world order that Trump is fashioning.

“Trump’s policies have really forced a lot of countries that have alliances with the US to start thinking about how their security arrangements would look without the US and what are the alternatives,” says Lauren Richardson, head of the Asia-Pacific College of Diplomacy at Australian National University (ANU) in Canberra. “It could really end up being America alone.”

The president’s disdain for a commitment made by his predecessor had international observers shaking their heads. “It tells other countries … that the US can’t be trusted to keep its word from one administration to another,” says Makau Mutua, chairman of the Kenyan Human Rights Commission. “That is not how great powers conduct policy.”

Washington’s threats to punish foreign firms that continue to do business with Iran, as their governments seek to keep the nuclear deal alive, has prompted an indignant response from Europe, whose leaders all support the 2015 accord. It is “unacceptable” that the US is acting “like the planet’s economic gendarme,” French Finance Minister Bruno Le Maire declared last week.

The reality of US global economic and military clout means European nations perhaps have little choice but to accept US dictates. Elsewhere in the world, though, as Trump shows scant regard for anyone else’s opinions, China and Russia are nibbling at the edges of the US mantle of global leadership.

There are fears, says Ian Lesser, head of the German Marshall Fund Brussels office, that “a world without American leadership in key areas is going to be a world in disorder.”

Going it alone, but where?

Last week’s decision to withdraw from the multilateral deal with Tehran was not the first time the Trump administration has preferred to go its own way in the face of almost universal international condemnation. Last June, Washington pulled out of the Paris climate change accord; the US is the only country to reject it. This week, the US moved its embassy in Israel to Jerusalem; so far only Guatemala has followed suit.

And Trump is bucking the international trading system, threatening to slap tariffs not only on China but on allies such as Canada, the European Union, and Japan. He ditched a 12-nation Asia-Pacific free trade deal as soon as he took office, leaving the other members to proceed on their own.

Over the years the US has failed to ratify a good number of international treaties that it had signed. But only once before the current administration had the country withdrawn from an accord that it had previously entered with force of law: in 2001, George W. Bush pulled out of the Anti-Ballistic Missile treaty with Moscow. (In March, Russian President Vladimir Putin linked his government’s drive to build a new generation of nuclear missiles to Mr. Bush’s decision.)

Trump supporters abroad (to be found mainly in Israel and Saudi Arabia) have welcomed his reversal of Barack Obama’s signature achievement as evidence that the US president is a man of his word. “He said he would walk out on the deal, and he walked out on the deal,” points out Meir Javedanfar, a lecturer at the Interdisciplinary Center Herzliya in Israel.

Most international observers, though, fear that the move makes US policy dangerously unpredictable. “Now it looks like the Americans can just withdraw from [an international agreement] if a new president comes who doesn’t like this or that about it,” says Vladimir Zharikhin, an analyst at the Russian Academy of Sciences in Moscow. “Nobody can be sure of anything if the American mood changes.”

At ground zero of the immediate crisis, Iran, deep mistrust of Washington has been widespread since the CIA organized a coup in 1953. The Islamic revolution in 1979 made hostility to the US a national ideology, and the 444-day takeover of the US Embassy in Tehran sealed many Americans’ mistrust of Iran. Now, Trump’s decision has strengthened the hardliners who never liked the compromises that Tehran made under the deal to get sanctions lifted.

Iran's supreme leader, Ayatollah Ali Khamenei, argued consistently that Western powers could not be trusted to keep their word. “Even Ayatollah Khamenei could not have known how the heavens would oblige to prove him right in his skepticism about the US,” says Ali Vaez, an Iran analyst at the Brussels-based think tank International Crisis Group.

The (nuclear) fallout

Following the fate of the Iran nuclear deal with particular interest is Kim Jong-un, the North Korean leader due to meet President Trump next month to negotiate his own denuclearization deal. Will the manner in which Trump reneged on the Iran agreement give him extra pause for thought about the value of any North Korean accord with the US?

Korean Central News Agency/Korea News Service/AP US Secretary of State Mike Pompeo (l.) shakes hands with North Korean leader Kim Jong-un during a meeting at Workers' Party of Korea headquarters in Pyongyang, North Korea.

Probably not, thinks Tong Zhao, who researches nuclear policy at the Carnegie-Tsinghua Center for Global Policy in Beijing – because Mr. Kim does not trust Washington in any case. “North Korea has always planned on trusting its own [nuclear] deterrent rather than any US security guarantee,” Dr. Tong says.

But the Iran example “will give North Korea a better excuse to say to the US president ‘Look, I can hardly trust you, so any denuclearization process has to be a long process of engagement and trust-building,’” he adds. “It undermines, rather than strengthens, American negotiating leverage.”

On the other hand, argues the ANU’s Dr. Richardson, Trump’s firm stance on the Iran agreement suggests “he is not going to have a lot of patience with denuclearization,” and that if he doesn’t get his way “the US will very quickly slap [Pyongyang] with sanctions and abrogate the deal. That must be pretty worrying for Kim Jong-un.”

On the other side of the world, in Mexico, editorialist Enriqueta Cabrera of El Universal, a Mexico City daily, was unambiguous in her judgment that “Washington’s decisions have turned the US into a partner that can no longer be trusted.”

The key issue for Mexico is the North American Free Trade Agreement (NAFTA), which Trump has threatened to tear up unless Mexico and Canada meet his demands for a revised deal.

“NAFTA is the real litmus test for whether it is America First or America Alone,” says Eric Farnsworth, vice president of the Council of the Americas, a group promoting democracy and free trade. The 1994 accord is “the bedrock of US hemispheric policy,” he adds. “If you cut out that foundational piece, what are you left with?”

In Latin America, where governments have long doubted whether Washington has their best interests at heart, Trump’s insistence on a deal on his terms – “my way or the highway” – is fueling mistrust. “In the [negotiating] game of give and take, there is no balance,” complains Analicia Ruiz, an expert on US-Mexican relations at Anahuac University in Mexico City.

The Canadian government is also “deeply worried” by the Trump administration’s international posture says Janice Stein, a veteran foreign affairs analyst at the University of Toronto. “We are also more vulnerable” because of Canada’s heavy economic dependence on the US market, she points out.

Who needs allies?

Trump’s distaste for NAFTA and other multilateral free trade deals is a sign of his reluctance to be constrained by the sort of rules-based order on which the world has functioned since World War II. In the administration’s enthusiasm for acting solely in America’s own interests, “it seems they are picking quarrels with the entire world, aiming to isolate themselves,” says Andrei Klimov, deputy head of the international affairs committee in the Federation Council, Russia’s upper chamber.

David Lawder/Reuters Canadian Foreign Minister Chrystia Freeland speaks with reporters after meeting with US Trade Representative Robert Lighthizer to discuss NAFTA autos negotiations in Washington, D.C., on April 25.

At the very least, the Trump administration is paying little or no attention to Washington’s traditional allies. The president ignored pleas by French President Emmanuel Macron, German Chancellor Angela Merkel, and British Prime Minister Theresa May to save the Iran deal, and in the Middle East “there is definitely a feeling” among US-friendly governments in Jordan and elsewhere “that the current administration is not listening to the advice coming from its allies in the region,” says Nabil Sharif, a former Jordanian cabinet minister.

In Europe, people are wondering whether Donald Trump thinks America needs allies in order to rule the world. The cover of the current edition of Der Spiegel, a German news-magazine, shows Trump as the raised middle finger of a hand, with the caption “Goodbye, Europe!”

Fears are running high that Washington will impose sanctions on European firms if European governments try to keep the Iran deal alive, forcing companies such as Airbus and Total to choose whether to do business in Iran or the US.

“I don’t think European governments or businesses are going to want to put their global commerce in jeopardy over a point of principle on the [Iran] agreement,” says Mr. Lesser.

“The European Union has practically always hesitated to confront the United States,” notes François Nicoullaud, a former French ambassador to Iran. “Europe’s involvement with the United States cannot be compared with its involvement with Iran. At the end of the day, the choice is quite clear.”

Europe and the US have a huge amount in common economically, politically, and in the security sphere, says Lesser. But as differences over issues such as Iran, climate change and trade mount up “it poses the risk of a broader disintegration in trans-Atlantic cooperation,” he says.

Already the signs of strain are showing, and the Europeans are not the only ones to suffer the consequences, says Huang Jing, former head of the Center on Asia and Globalization at the Lee Kuan Yew School of Public Policy in Singapore.

If Trump wants to drive a hard trade bargain with Beijing to protect US property rights and technology, he will need European support, Dr. Huang argues. But “because of the Iran deal, the US has totally lost its solidarity with European countries.”

At the same time, Huang adds, Washington’s major Asian ally, Japan, is unnerved by signs of US unreliability and is hedging its bets. Prime Minister Shinzo Abe has made an obvious effort to improve Tokyo’s relations with Beijing and even with Russia. “Japan has been preparing for this unpredictability,” he says.

Carrots or sticks?

Trump’s withdrawal from the Iran deal, coming on top of earlier decisions, has broken the traditional mold of US global leadership that Washington exercised through a network of alliances and institutions. Together they comprised a system built around rules. Now, the US president seems to be counting more on America’s raw power to lay down the law and demand that other countries abide by it.

That is the message of the secondary sanctions that US officials are threatening against any foreign firm that does business with Iran: the sanctions will punish other countries for not agreeing with a unilaterally declared US policy.

The US has the power to do that sort of thing, but it fosters resentment. And the US role in the world is facing challenges.

Even in America’s traditional “backyard”, Latin America, where US dominance is still clear, “new poles of leadership” are emerging, says Mr. Farnsworth, evidenced by rising Chinese investment in the region.

Such investment – and influence – is even more pronounced in Africa, where the Chinese model of authoritarian capitalism appeals to many local rulers and where Trump’s actions are puzzling. “I foresee a situation where African countries will prefer China to the US as an ally,” says Benon Mukundera, an international relations scholar at Kampala University in Uganda. “You do not want to keep a friend who does not keep his word.”

Nowhere is the gathering challenge to US leadership clearer than in the region of the world where Washington has traditionally wielded the greatest clout – the Middle East. “A majority of countries in this region … are looking for US leadership,” says Mr. Javedanfar, the Iranian-born Israeli lecturer and commentator. “And they see Putin stepping in because there has been a void in regards to US leadership. If there is one concern in Israel it is, ‘What is Trump’s Syria strategy?’ Because he does not seem to have one.”

Most strikingly, Moscow has taken over from Washington the role of chief broker in Syrian peace talks and leading outside power. But with Middle East peace and stability apparently not at the top of the US agenda, and with Trump adopting an unabashedly uncritical attitude to Israel, regional powers are stepping up.

Turkey, for example, has adopted a strongly pro-Palestinian stance to forge new ties in the Arab world, and it is building a military presence in the region for the first time. Ankara is planning to station naval vessels and fighter jets in Qatar later this year. Even Egypt, which has been totally dependent on the US for economic and diplomatic support since it made peace with Israel in 1979, is now looking elsewhere.

“America is still a superpower, it still is influential in the Middle East, it still has strong allies in the region, but it is displaying no leadership,” says Oraib Rantawi, head of the Amman-based Al Quds Center for Political Studies, a think tank. “Whether it be getting Israelis and Palestinians to the negotiation table, saving the Iran nuclear deal, or ending the wars in Yemen and Syria, no one is going to the Americans,” he adds.

At the moment it is the Europeans who are feeling the brunt of Donald Trump’s new style. As they wrestle with the prospect of US sanctions should they stick to the Iran nuclear deal, European leaders are beginning to contemplate life without the security blanket of US leadership.

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Divisions within Europe are legion, and Chancellor Merkel may have been voicing only a pious hope last week when she insisted that “Europe has to take its destiny into its own hands. That is the task for the future.” But it reflected a bitter conclusion Merkel said she had reached. “It is no longer the case that the United States of America will simply protect us.”

• Michael Holtz in Beijing; Sara Miller Llana in Paris; Scott Peterson in London; Whitney Eulich in Mexico City; Taylor Luck in Amman, Jordan; Fred Weir in Moscow; Dina Kraft in Tel Aviv; Mark Oloo in Nairobi, Kenya; and Dylan C. Robertson in Ottawa contributed to this article.