When he quit the deal last week, US President Donald Trump gave businesses a maximum of six months to wind up operations in Iran or face swingeing penalties under American sanctions.
According to Ms Mogherini, the deal is capable of surviving without U.S. support as long as Iran continues to agree to stand by it.
Germany and France joined him in reiterating their commitment to the deal, which restricts Iran's nuclear capabilities in return for the lifting of economic sanctions.
Criticism of the USA sanctions also came from the United Kingdom, which resumed its trade with Iran after the deal was struck. In 2015, French lender BNP Paribas was slapped with a $9 billion fine after USA prosecutors accused it of violating sanctions against Iran as well as Sudan and Cuba. The International Atomic Energy Agency (IAEA) has said all along that Iran has met its nuclear commitments.
The announcement by Donald Trump that the USA would pull out of the agreement came with the restoration of sanctions against Tehran, including six individuals and three companies it claims are funnelling millions of dollars to the Islamic Revolutionary Guard's elite Quds Force.
Iranian President Hassan Rouhani asked the European Union to stand against the United States' "illegal and illogical" actions, saying that Tehran could stay in the accord only if it fully benefits from it. But Trump and other Republican Party leaders, apart from Israel, kept condemning the deal, which Trump described last week as "decaying and rotten".
It also demanded that Iran cease supplying weapons to the Houthi rebels, who have been at war with Tehran's archenemy Saudi Arabia, end cyberattacks against the USA and its allies, stop menacing US military ships in the Persian Gulf and abandon its rhetoric about destroying Israel. Antipathy towards Obama is a part of Trump's psyche.
German Foreign Minister Heiko Maas said that "it won't be easy, that's clear to all of us". And he couldn't even win that war.
Putin has already spoken with German Chancellor Angela Merkel and Turkey's President Recep Tayyip Erdogan about efforts to save the accord, after voicing his "deep concern" over Trump's decision.
Ominous was the response of Jean-Claude Juncker, president of the European Commission, who was quoted as saying the United States "no longer wants to cooperate with other parts in the world", and that it is now turning its back on multilateral relations "with a ferocity that can only surprise us".
"We all agreed that we have a relative in intensive care and we all want to get him or her out of intensive care as quickly as possible", European Union foreign policy chief Federica Mogherini told reporters after the 90-minute meeting.
Iran is now seeking assurances from other signatories of the Treaty that they will remain faithful to its provisions.
Describing the deal as "hard-earned", Mr Yi added: "I hope and believe that these visits to multiple countries will help protect Iran's legitimate national interests and peace and stability in the region". "We're on the right track to ensure that the interests of all parties, especially Iran, will be secured", he added.
The EU's executive arm, the European Commission, has been examining measures to counter the introduction of any USA sanctions that might harm European businesses and is expected to unveil them to EU leaders at a meeting in Bulgaria on Wednesday.