"I cannot talk about legal or economic guarantees but I can talk about serious, determined, immediate work from the European side", Mogherini said.
He said British and European officials would meet in Brussels on Tuesday to discuss ways to protect companies against US sanctions on Iran, which will be phased in over the next six months.
Calling the accord as an "embarrassment" that was "defective at its core", he also warned of severe consequences if Iran resumes its nuclear programme.
But last week US President Donald Trump announced he was leaving the deal and reimposing sanctions.
Mr Khamenei said that while Iranian officials "want to continue the nuclear deal" with Britain, France and Germany, he "did not trust these countries either". All 15 UNSC members have endorsed the Iran deal, enshrining it through a resolution as part of worldwide law.
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Despite the lack of support from other world powers, Bolton said he thought the US sanctions would make a dent in and of themselves. Congressional leaders were split on whether the U.S.'s deal was sound. The deal's proponents say it is crucial to forestalling a nuclear Iran and preventing wider war in the Middle East.
Iran's nuclear chief Ali Akbar Salehi was quoted by Fars news agency as saying he was not optimistic on the prospects of the talks with the Europeans.
Said Iran's Zarif: "We are on the right track".
While Israel was strongly in support of President Trump's decision, Britain, France and Germany came out against the withdrawal. Despite the private doubts among many European diplomats, their governments will say that they are sticking by the 2015 accord that gave Tehran sanctions relief in return for an end to its nuclear ambitions.
"It is vital that we continue to engage with the United States and continue to interrogate our friends in Washington about how they see the nuclear deal developing".
Zarif said the latest US decision was "illegal". They would have had us believe there was no risk, that we would be in far worse shape without the JCPOA than with it. However, Treasury Secretary Steven Mnuchin said last week that Washington "will continue to work with our allies to build an agreement that is truly in the best interest of our long-term national security". To preclude that, Washington should create a channel with Europe to find a way to focus on areas of non-nuclear common interest in the post-May 8 world that involve Iran, like stopping ballistic missile flight tests.
Mogherini said Iran's President Hassan Rouhani has reconfirmed to her that Tehran will not pull out of the agreement if other signatories (not just France, United Kingdom, and Germany but also China, Russia) remain committed to its terms. The thing is, some of the other six countries involved in this are making billions through trade with Iran, and for that reason and others, want to keep their part of the deal intact.