Reacting to Trump's decision, Tehran said it would for now stay in the deal, pending talks with Russia, China and the three European signatories before coming up with a decision on the future of the deal.
Major European powers have sought to keep Iran in a landmark worldwide nuclear agreement after President Donald Trump pulled the US out of the pact and promised tough economic sanctions against Tehran.
The Europeans and Iranians have now tasked experts to come up with measures quickly and will meet again in Vienna next week at a deputy foreign minister level.
Zarif's statement puts pressure on U.S. European allies and other parties to the deal to find a way to keep it alive despite Trump's efforts to ice it, said Suzanne Maloney, an Iran analyst at the Brookings Institution.
The president made the same claim in announcing his decision to pull the United States out of the Iran nuclear agreement earlier this week - an assertion that fact checkers have called "exaggerated" and lacking crucial context.
The US says firms have six months to halt business and can not enter into new contracts or they will face sanctions. "In the current situation, it seems the apparent conflicts between the U.S. and the three European states over the fate of the JCPOA are in fact a labour division made among them".
Zarif's statement said that with the US withdrawal from the deal, Iran is prepared to embark on the 2025 enrichment project now.
However, the European Union (EU) is now rushing to shield Iran from these sanctions.
"We consider ourselves as one of the participants in the accord and we are going to fulfil it and are in close contact and dialogue with all the other participants", Ryabkov said.
It is unclear how well the measure could be enforced, given that big multinationals are likely to be doing more business in the US than they are in Iran and may be unwilling to compromise that market access.
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.
Mr Le Drian said the commitment of other partners to the Iran deal should be respected.
And while other countries have not leapt into following the US' example, Bolton and Pompeo are confident that European leaders will eventually join the USA in sanctioning Iran and withdrawing companies from the region.
He added: "As the president of the republic has said, we are ready for all option (s)".
"If the nuclear deal is to continue, the interests of the people of Iran must be assured", Zarif added. Mr Trump pulled out of the accord on May 8, saying that Iran had violated the spirit of the deal by financing militant activity in the Middle East and by continuing to test ballistic missiles.
"We do not see ourselves as a mediator between Iran and the USA", he said.
Each company and bank will have to decide whether to risk being cut off from the US financial system. "It's clear that there should also be economic incentives - that will not be easy after the USA decision", Maas said.
But even if Europe goes forward with such confrontational measures, its corporations might still see little profit in jeopardizing their access to the American market: Most companies have much less to gain by embracing Tehran than to lose by alienating Washington; America's banking system is more valuable than Iran's oil fields. European countries say Trump's decision will raise the risk of conflict in the region.