The long-running nuclear dispute was in the focus of talks between Russian President Vladimir Putin and the Islamic Republic's top nuclear negotiator, Ali Larijani. Lavrov and Igor Ivanov, Russia's Security Council chief, also attended the talks.
"We have reached agreement to continue our contacts, and we will work to achieve our common goal of resuming talks with six nations," Lavrov said
The five permanent UN Security Council members plus Germany - Iran-6 negotiators - offered Tehran a package of incentives in June in a bid to entice Tehran to halt uranium enrichment, the process crucial for both power generation and weapons production. But Iran refused, citing its rights under the Nuclear Non-Proliferation Treaty.
Lavrov said Russia will continue contacts with the six negotiators in the nearest days and will hopefully find a mutually acceptable basis for further talks.
The Security Council is discussing sanctions against defiant Iran drafted by Britain, France, and Germany.
The EU-3 proposed a ban on sales of missile and nuclear technologies to the country, freezing its military bank accounts, and imposing visa restrictions on Iranian officials linked to the nuclear industry. Russia, Iran's major trade partner, has called the sanctions excessive.