The legitimate interests of each participant in the Iran nuclear deal are enshrined in the Joint Comprehensive Plan of Action and the parties need to cooperate in defending them, he said.
"With the nuclear deal in place we have better chances to address any other issue.with Iran", Mogherini said.
US President Donald Trump signs a document reinstating sanctions against Iran after announcing the US withdrawal from the Iran Nuclear deal.
US President Donald Trump said on Tuesday that the United States was withdrawing from a 2015 deal negotiated by the Obama administration.
"I think you have to start first with the fundamental deficiencies of the deal itself", Bolton said.
The European Commission has been examining measures to counter the introduction of any US sanctions that might harm European businesses and is expected to unveil them to EU leaders at a summit in Sofia, Bulgaria, on Wednesday.
French Foreign Minister Jean-Yves Le Drian said on Tuesday the Middle East was explosive and could be on the cusp of war.
Former Defense Secretary Robert Gates said while the Iran deal was "a flawed agreement" because of a lack of unfettered inspections and other problems, leaving the deal isolates the United States and Trump should have extended it for at least another six months to work with allies. "We simply committed to fully comply with all the commitments taken there, which means for the Iranian side the nuclear-related commitments, and from our side and from the side of the rest of the global community, in particular the commitments related to the economic benefits the Iranian people need to see as an outcome of their own implementation of the Iran deal".
Zarif was returning from a diplomatic tour of the remaining parties to the 2015 nuclear agreement - Britain, France, Germany, China and Russian Federation - following the United States decision last week to pull out.
White House National Security adviser John Bolton on Sunday said USA sanctions on European companies that do business with Iran were "possible, but Secretary of State Mike Pompeo said he remained hopeful Washington and its allies could strike a new nuclear deal with Tehran".
"Unfortunately once again we see that Washington is trying to revise key worldwide agreements as it happens to Joint Comprehensive Plan of Action, as it happens to Jerusalem (al-Quds) problem and a number of other agreements", the top Russian diplomat said.
The EU is also looking at how it could develop special financing vehicles for doing business with Iran.
Washington has long complained that the nuclear deal does nothing to stop Iran's ballistic missile programme or its interference in conflicts across the Middle East from Syria to Yemen.
German exports to Iran totalled almost 3 billion euros in 2017, while French exports soared from 562 million euros in 2015 to 1.5 billion in 2017 and oil giant Total has pledged to invest some $5 billion in the South Pars gas field.
"We have to accept, be realistic about the electrified rail, the live wire of American extraterritoriality and how that can serve as a deterrent to businesses", Johnson said.
Pre-existing U.S. sanctions against Iran have hit European Union firms, with large fines imposed since 2009 on European Union banks with USA subsidiaries, such as HSBC, Standard Chartered, ING, Barclays, Credit Suisse BNP and Lloyds.