The US President also pledged to reinstate the sanctions against Iran, which were lifted as part of the agreement.
Zarif was in Moscow to meet Russian Foreign Minister Sergei Lavrov on Monday, a day after visiting Beijing.
Meanwhile, speaking on the phone with French President Emmanuel Macron on Wednesday, Rouhani said Europe has a very limited time to save the pact and must determine and announce its clear, firm stances on its obligations in the deal. "We will have to discuss that with Iran". Moscow has close ties to Tehran.
Le Maire said he was seeking US exemptions for French countries already present in Iran, including Renault, Total, Sanofi, Danone, and Peugeot.
The European members of the deal are trying to keep it alive without the U.S. Yet it's unclear that will be workable, because Trump has vowed to punish European companies that continue doing business with Iran despite re-imposed U.S. sanctions.
"The Russian side underscored its commitment to preserving the agreement", the statement said, emphasizing that Russia holds "interests of ensuring bilateral cooperation" with Iran.
"Since the signing of the JCPOA (nuclear deal), we have gone from an atmosphere like a gold rush, to one of utter depression", said a Western trade diplomat on condition of anonymity.
Iran's foreign minister departed for China on a whirlwind diplomatic tour early on Sunday, as world leaders scramble to salvage something from the wreckage of a landmark nuclear deal in the wake of the United States' withdrawal.
Other European companies with big Iran deals and significant operations in America are giving little away about their plans.
Trump not only has undone United States participation in global climate deals but also has scrapped domestic environmental regulations.
In his statement, Zarif accused Trump of "ignorance and folly" and said American foreign policy had "dragged the Middle East into chaos".
Britain, France and Germany led a campaign to persuade Trump to stick with the deal negotiated by his predecessor Barack Obama.
The European ministers also brought up in the talks their concerns over Iran's ballistic missile program and regional activities, diplomats said.
Exports of German goods to Iran rose by around 400 million euros to 3 billion euros.
"We are ready to talk to all the companies concerned about what we can do to minimize the negative consequences" of the USA sanctions, German Economy Minister Peter Altmaier told Deutschlandfunk radio. USA officials were reaching out Tuesday to central banks in other countries in the Middle East and Europe to inform them of the sanctions and encourage them to immediately freeze assets the bank has overseas.