Lavrov said at a meeting with the Iranian foreign minister that it is necessary to prevent any new threats to the nuclear non-proliferation regime.
Russia and a number of other countries have legitimate interests in the Iranian nuclear deal and they must be jointly defended, Lavrov said.
"We have planned contacts with all parties to this deal, except for the United States which announced the withdrawal from the agreement, in the coming days," Lavrov said.
Mohammad Javad Zarif said that the balance within the JCPOA was altered following the US withdrawal from the multilateral agreement. He added that Iran would discuss ways to cooperate in a 4+1 format within the JCPOA.
"Russia's position is encouraging for us. I hope that today I will be able to hold consultations with you on the ways of cooperation in the 4+1 format," Zarif said at a meeting with Lavrov.
"Unfortunately, the protest against international rules and laws has become a habitual practice for the US government. … The JCPOA corresponds to the balance of commitments between the Iranian side and Europe and, in particular, the United States, and of course this balance has been undermined after the US withdrawal," Zarif said.
Iran has expressed its opposition to Trump's move.
German Chancellor Angela Merkel and her French counterpart, Emmanuel Macron, have also expressed concerns over Washington's decision.
The Iranian nuclear deal was reached in 2015 between Iran and the P5+1 group, comprising the five permanent members of the United Nations Security Council (China, France, Russia, the United Kingdom and the United States), plus Germany, and the European Union.