America’s three closest friends in Europe — Britain, France and Germany — are near-bursting with anger and exasperation at the United States. In a frenzy of meetings and phone calls among them over the past week, their leaders have tried to figure out what they can do about President Trump’s withdrawal from the nuclear agreement with Iran and his plans to impose sanctions on their companies that continue doing business there.

The answer, they fear, is not much.

They can retreat in sullen bitterness, as one European official put it, but they realize that would accomplish little.

They can ask for exemptions to the sanctions that the administration has said will be applied to any European business that trades with both Iran and the United States. But they have been told, with humiliating clarity, that there will be no exemptions.

World leaders slammed President Trump's May 8 announcement that the United States would leave the Iran deal, but Israel's prime minister lauded it. (Sarah Parnass/The Washington Post)

They can look for ways to preserve the deal by extending financing and other guarantees to European investment in Iran. But even if those mechanisms worked — and there is little belief that they would — the Europeans have not yet decided how far they are willing to go in antagonizing Trump.

They are determined, British Foreign Secretary Boris Johnson said Monday after a meeting with his French counterpart, “to conserve the essence” of the nuclear deal without the United States. On Tuesday, the three European powers will meet in Brussels with European Union officials and with Iranian Foreign Minister Mohammad Javad Zarif to discuss “exactly how we propose to get on with it,” Johnson said.

On Wednesday, government heads of all 28 E.U. countries will gather in Sofia, Bulgaria, where they will talk about the Iran agreement and their separate beef with the United States over looming steel and aluminum tariffs.

The Post’s Alan Sipress and Karen DeYoung explain how President Trump’s decision might affect an already tense Middle East. (Sarah Parnass, Joyce Lee/The Washington Post)

But they are hesitant to deepen the wound, even as they want the United States to take responsibility for healing it. “It’s vital that we continue to engage with the USA and continue to interrogate our friends in Washington,” Johnson said, to find out how the administration intends to achieve what Trump says he wants — a new deal with Iran that fixes the flaws of the old one.

So far, the officials say, they have no idea how the administration plans to accomplish that. “We haven’t heard anything that is close to a strategy,” said one of several European officials who discussed the sensitive subject on the condition of anonymity.

In Trump’s announcement of withdrawal from the deal last Tuesday, and in a follow-up media briefing by national security adviser John Bolton, the administration said it wanted to immediately start talks on a new deal. Bolton, as promised, called his British, French and German counterparts Wednesday. But those conversations, the European officials said, focused almost entirely on U.S. insistence that there would be no sanctions exemptions for European companies.

In a Sunday interview with CNN, Bolton showed little patience for European concerns. The nuclear deal had worsened, rather than improved, Iran’s behavior in the region, he said. “It’s ludicrous to suggest that Iran feels less constrained,” he said. “I would argue that they felt they could act with impunity. They watched. They watched Europe put exactly zero sanctions on their missile program” since the 2015 agreement was signed.

When Secretary of State Mike Pompeo called his European counterparts last weekend, all were eager to hear the administration’s plans. Instead, officials from two of the big three allies said, he threw the ball in their court, asking how they saw the future unfolding.

“But it’s up to the administration to come up with a framework, a new position,” a second European official said. “We are waiting for them.”

The impression so far from Bolton and Pompeo is that the administration envisions a broad coalition against Iran, including Israel, the Persian Gulf states and Iran’s major trading partners in Asia, and may not even think it needs Europe. “We’re not going it alone,” Bolton said. “We have the support of Israel. We have the support of the Arab oil-producing monarchies and many others. . . . I think the issue here is what the Europeans are going to do.”

While the regional partners are eager to be part of a pressure campaign and even a military one, should it come to that, countries such as China — which has just opened a major new rail line into Iran and has said it plans to continue normal trade — are not interested in confronting Iran.

In Europe, while allies say they agree with the need to stem Iran’s destabilizing regional activities and ballistic missile programs, the focus for the time being has been to reassure Iran that they will not abandon the deal. The government in Tehran has said it’s waiting to be convinced that they can continue to make it work, despite U.S. pressure.

Trump’s continuing effort to circumvent global rules has thrown the multilateral order into “real crisis,” German Chancellor Angela Merkel said Friday in a speech to a religious conference.

“If we always say that something doesn’t suit us, and we don’t get a new international order, and everybody simply does what they want — then that’s bad news for the world,” she said.

Others in Merkel’s government have suggested there is little basis for trust in any future talks with the United States. Deputy Foreign Minister Niels Annen recently told the German magazine Der Spiegel that the administration had shown “very little willingness to take the arguments of its allies seriously.”

Just as Trump has emphasized his campaign pledge to withdraw from the deal, the Europeans all have their own political realities to contend with.

In Germany, where government historically is by coalition, a vast majority sees the United States under Trump in an unfavorable light, with just 11 percent expressing confidence in the president’s leadership, according to the Pew Research Center.

Trump is similarly unpopular in France, and President Emmanuel Macron’s state visit to Washington — during which the two leaders exchanged a number of physical touches — was roasted in the French press, with Macron portrayed as an obedient child.

The domestic consequences of pursuing any new agreement with Washington would probably add to the perception of Macron as too weak to face up to Trump.

The Europeans spent months negotiating with the State Department about supplements to the Iran deal that would accommodate concerns Trump expressed in January. By late April, senior officials on all sides said they were close to agreement.

Yet when Macron, Merkel and Johnson traveled to Washington in the days and weeks before Trump’s announcement, all came away with the feeling Trump had not read the five-page document they had prepared and perhaps was even unaware of the effort.

In Brussels, where the E.U. is headquartered, many are skeptical that any further discussion is possible with the United States. When officials meet there Tuesday, talk is expected to focus on what they can do to keep Iran from abandoning the deal, rather than how to accommodate the United States.

Michael Birnbaum in Brussels, James McAuley in Paris and Griff Witte in Berlin contributed to this report.