"We are witnessing another spiral of violence that must be stopped at all costs, which requires patience and wisdom from both sides," Lavrov said following talks with his Israeli counterpart Tzipi Livni.
He added that relations could only be normalized if both sides made efforts.
"Therefore, we call on the Israeli government to show the maximum restraint," Lavrov said, adding that both conflicting sides and the international community should pursue a responsible policy to normalize the situation in the Middle East.
"We expect and hope that the Road Map plan will be implemented," he said, adding that his talks would also hopefully bring some progress on the issue.
Israeli Foreign Minister Livni said Israel would not let to make terrorism an instrument for attaining goals in the Middle East, which she said was a signal the Palestinian authorities.
Livni said that the kidnapping of an Israeli soldier by Palestinians last week had shown the real character of the radical Palestinian movement Hamas, which was elected to govern the country in January. Israel has not recognized the new government because Hamas had claimed responsibility in the past for a number of terrorist attacks in the region, and is on the list of terrorist organizations both in Europe and the United States.
Russia, which along with the U.S., UN and EU is a mediator in the Middle East peace process, invited a Hamas delegation to Moscow in a move that was heavily criticized by Israel and the other mediators in the Quartet.
The Quartet has demanded that Hamas recognize Israel, renounce violence and meet commitments pledged by previous Palestinian leaders.
Hamas has refused to recognize Israel, saying talks can only resume after the Israelis withdraw from the Palestinian lands occupied in 1967 and agreed to Palestinian refugees' return there. At the same time, Hamas leaders admit that contacts with Israel are vital because the country has handed over tax and customs revenue worth at least $50 million that it has collected on behalf of the Palestinians.