But even as Pompeo talked up coordination with America's allies, Trump's new National Security Advisor John Bolton reminded Europe over the weekend that its companies could face sanctions if they continue to do business with the Islamic republic.
The 2015 deal had placed unprecedented restrictions on Iran's nuclear program in exchange for billions of dollars in sanctions relief.
"Today we hope to see how we can use the available mechanisms not to allow the undermining of this important document with the participation of European Troika, China, Russia, Iran and European Union", he stressed.
French Foreign Minister Jean-Yves Le Drian, speaking in Dublin, declared: "We are stakeholders" and will remain so.
Germany said it will spend the next few months trying to persuade Washington to change its mind.More news: Navalny Gets 30 Days In Jail For Anti-Putin Protests
"The only way to avoid pain from these sanctions is negotiating with the USA, but the instruments are not easy to find", Volker Treier, deputy managing director of Germany's Association of Chambers of Commerce and Industry, said in an interview.
The EU, which with Germany, France, Britain, Russia, China and the United States, signed the nuclear accord with Iran, does have some steps it can take to shield European business in Iran. "It depends on the conduct of other governments".
The accord lifted worldwide sanctions on Iran in 2016 in return for Tehran shutting down its capacity, under strict surveillance by the United Nations nuclear watchdog, to stockpile enriched uranium for a possible atomic bomb.
The White House said Trump had spoken with French President Emmanuel Macron on Saturday and "reiterated the need for a comprehensive deal that addresses all aspects of Iran's destabilizing activity in the Middle East". "Now, that will not happen!"
With Chancellor Angela Merkel warning that faith in the worldwide order is at stake, Germany, France and the United Kingdom are embarking on a diplomatic mission to salvage what they can of the accord, both to keep Iran on side and to shield European companies from US sanctions that threaten billions of dollars of investment.
After an hour-long meeting at European Union headquarters in Brussels, Mr Zarif said he believed both sides were "on the right track" to make sure that the interests of the deal's "remaining participants, particularly Iran, will be preserved and guaranteed".More news: White House dumps 'cyber czar' advisory position
"In this time, we'll use all possibilities to persuade the USA government to change its behaviour", he told ZDF television.
It called on "the global community and the countries that are partner to the nuclear agreement to agree with Trump's position for the removal of nuclear weapons and other weapons of mass destruction from the region, in order to preserve worldwide security and stability". Macron told Trump in their telephone call on Saturday that he was anxious about stability in the Middle East, according to Macron's office.
White House national security adviser John Bolton says "regime change" in Iran is not now part of the administration's policy, despite his past suggestions that the United States should push for a new government in Tehran.
The deal's proponents say it is crucial to forestalling a nuclear Iran and preventing wider war in the Middle East.
Trump spoke with British Prime Minister Theresa May on Friday, and "both leaders condemned the Iranian regime's provocative rocket attacks from Syria", the White House said.
"I think it was testing the limits of the deal's provisions, exceeding them in some cases", Bolton said.More news: Scientists Claim Multiverse May Sustain Life