Following meetings with top European Union representatives, as well as officials in China and Russia, Iran's Foreign Minister Javad Zarif is confident that the nuclear deal can be salvaged.
European Union experts have already started work on measures to get round United States sanctions on Iran, Mogherini said.
The steps forward underscored the EU's hopes that diplomacy and the promise of economic benefits might keep Iran in the fold of a nuclear deal that Europe sees as essential to security.
Major European powers and Tehran committed Tuesday to keep working together to save the Iran nuclear deal despite U.S. President Donald Trump's determination to kill it off.
German Chancellor Angela Merkel has acknowledged that the Iran nuclear deal "certainly has weaknesses" but says it should be preserved.
"It won't be easy, that's clear to all of us".
Many Europeans, like Ms. Tocci, believe that the unstated American aim is "regime change" in Iran, something that the British and French foreign ministers, Boris Johnson and Mr. Le Drian, have specifically ruled out as a European goal.
Brussels does have other issues it wants to address with Iran, Mogherini said, referring to Tehran's ballistic missile program and conflicts in Syria and Yemen.
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"I want to stress we are under no illusion about the stuff Iran gets up to in the region, in the Middle East". "One of the key things we will be talking about. we will be looking at all the ways that we can come up with to protect legitimate United Kingdom and European business who may want to trade with Iran".
"We are on the right track... to make sure that the interests of the remaining signatories of the JCPOA, especially Iran, will be guaranteed".
The European Commission has been examining measures to counter the introduction of any US sanctions that could harm European businesses.
When he quit the deal last week, USA president Donald Trump gave businesses a maximum of six months to wind up operations in Iran or face swingeing penalties under American sanctions.
"We have to be realistic about the electrified rail, the live wire of American extraterritoriality and how [it] can serve as a deterrent to business", Johnson told reporters in Brussels.
"As long as Iran respects the provisions of the deal, the EU will also respect it", said Donald Tusk, president of the European Council and chairman of the leaders' gathering in the Bulgarian capital Sofia.
The EU's top energy and climate official, Commissioner Miguel Arias Canete, is heading to Iran on May 18-21 for talks on energy cooperation, a symbolic gesture from the EU that it wants to stay engaged despite the US withdrawal.