He made the comments one day after a meeting in Moscow of diplomats from the five permanent members of the UN Security Council, plus Germany.
Lavrov said no decision had been adopted at the meeting, but, he said, all participants agreed that Iran must take "urgent and constructive steps" to ease concerns over its nuclear program.
Lavrov said that contacts would continue "in various formats so as to get this idea through to the Iranian leadership and to obtain a constructive response to these calls. That would open the way for the resumption of talks."
U.S. Undersecretary of State Nicholas Burns on April 18 said the participants were united "that Iran should hear a stiff message from the international community."
The United States accuses Iran of seeking to secretly build nuclear weapons and is calling for tough measures, including the possibility of sanctions.
Russia and China so far remain opposed.
Discussions on the crisis are expected to continue in Moscow today among envoys from the G8, the group of eight leading industrialized nations, which is currently headed by Russia.
(compiled from agency reports)
What Would Sanctions Mean?
MOVING TOWARD SANCTIONS: If the United Nations Security Council imposes sanctions on Iran, domestic support for Iranian President Mahmud Ahmadinejad will wane, according to ALEX VATANKA, Eurasia editor for Jane's Information Group.
Vatanka told a February 24 RFE/RL briefing that "economic sanctions will hurt the average Iranian" and, consequently, many "will blame the ruling clerics" for making life difficult and "impairing the country's long term development."
Vatanka said sanctions would be a serious challenge to the Iranian government. If harsh economic sanctions were imposed, Iran's poorest population will be hurt the hardest -- and might react "as they did in the 1970s and protest in the streets." Sanctions on travel, Vatanka said, would hurt a many Iranians because "Iran is a nation of small traders" who depend on the ability to travel to earn an income. According to Vatanka, unemployment in Iran is estimated at 30 percent, "so small trading is essential to survival." Although current U.S. sanctions "haven't worked," he said, "Iranians fear an oil embargo." He stressed that "oil revenues are a major part of the economy, so it is critical to look at this sector."
Should negotiations with the European Union and the UN fail, Vatanka believes that Iran would follow a "North Korea model," since Ahmadinejad's base of support among the "Islamist militias" has been "urging withdrawal from the NPT [Nuclear Non-Proliferation Treaty]." The Iranian government's "tactic" so far, Vatanka said, is governed by the belief that "by shouting the loudest, you'll get concessions [from the West]."
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THE COMPLETE STORY: RFE/RL's coverage of the controversy surrounding Iran's nuclear program.