There was no press conference following the Lavrov-Zarif talks in Moscow.
The landmark agreement was signed in July 2015 by Iran and the five permanent members of the United Nations Security Council - Britain, China, France, Russia and the United States - plus the European Union and Germany.
A Russian foreign ministry spokesman confirmed the pair would meet Monday morning.
Boris Johnson has held talks with his French and German counterparts as they work to save the Iran nuclear deal after the United States chose to withdraw from the agreement.
President Donald Trump signs a Presidential Memorandum on the Iran nuclear deal from the Diplomatic Reception Room of the White House, Tuesday, May 8, 2018, in Washington.
Washington's decision to withdraw from the deal and reimpose sanctions angered its European allies as well as China and Russian Federation.
Among things the European Union could consider, he said, are reinforcing a 1996 "blocking statute" that could allow companies to ignore sanctions.
"Let's not fool ourselves that are that dozens of things we can do", said a second senior European diplomat.
Despite complaints in European capitals, Mr. Bolton suggested that European allies might agree to new US approach once they digest Mr. Trump's decision and face the threat of sanctions.
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Are you excited for Stalker 2? A website recently popped up online displaying only an image that says S.T.A.L.K.E.R.2 and 126.96.36.199. CEO of GSC Game World Sergei Grigorovich announced in Facebook that is now being developed computer game S.
Now its stake in the project will probably be taken over by its Chinese partner, CNPC - Beijing, unlike Paris, is willing to challenge president Trump.
German Foreign Minister Heiko Maas said that "it won't be easy, that's clear to all of us".
The Prime Minister had already issued a joint statement with French President Emmanuel Macron and German Chancellor Angela Merkel to express their "regret and concern".
"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.
It reiterated that Iran was preparing to resume "industrial scale" uranium enrichment "without any restrictions" unless Europe provided solid guarantees it could maintain trade ties despite renewed USA sanctions.
European firms, especially those from France and Germany, rushed to invest in Iran following the 2015 accord, under which Tehran agreed to freeze its nuclear programme in return for an end to punishing global sanctions.
So far China, France, Russia, Britain, Germany and Iran remain in the deal; Morgherini claims she has received assurances from the Iranian government that it intends to uphold the deal.
The immediate impact is more likely to be seen in a tougher approach in Syria, where Iranian troops (sent to aid the government side in the civil war) are bombed by the Israelis practically every week.
The recent talks between the US and European diplomats on how to fix the current Iran agreement foundered on the question of how to address the easing beginning in eight years of the nuclear constraints.
Meanwhile, the USA imposed sanctions on Iran's central bank governor, Valiollah Seif, and Iraq-based Al-Bilad Islamic Bank for "moving millions of dollars" for Iran's elite Revolutionary Guard Corps, as Washington seeks to cut off funding for what it says is Iran's malign activities in the Middle East.