"We hear criticism of the Quartet of Middle East mediators. We think this criticism is justified, because the Quartet has long remained idle. We stand for activation of this site but not in its old format," Lavrov said at the Russian-Arab forum in Sudan.
The minister also said an Arab League representative with full-fledged member status could join the Quartet, because "the Arab peace initiative can pave the way for sustainable and long-term reconciliation."
"Hope these proposals will be heard by our Western partners," Lavrov said.
Earlier in July, Russia's envoy to the UN Vitaly Churkin said that the Quartet must be expanded with representatives from the Arab League.
Recently, the Quartet, established in 2002 and consisting of Russia, the United States, the United Nations, the European Union and the United Kingdom, has been accused of ineffectiveness amid lack of significant progress in peaceful relations between Israel and the Palestinian Authority.
The Arab League, a regional organization of 22 members, established in 1945, focuses on issues within the Arab world, and looks after member interests in economy, politics, culture and religion.
Time for UN Security Council to Discuss Palestinian Issue
Moscow believes that it is time for the UN Security Council to begin discussions on the Palestinian issue, Russian Foreign Minister Sergei Lavrov said Wednesday.
Direct talks between Israel and Palestine started in 2013 and were mediated by US Secretary of State John Kerry. Kerry suggested a plan, according to which the negotiations were supposed to last up to nine months, and the peace deal was set to be reached by April 29. The talks failed with both sides blaming each other.
The latest round of the Israeli-Palestinian talks was held this year in spring, but did not bring tangible results.
In October, Palestinians worked out a draft UN Security Council resolution that defines strict time limits for Israel to end its occupation and remove settlements before November 2016.
The State of Palestine has been recognized by 135 out of 193 member states of the United Nations.
Lavrov Plans to Meet US Secretary Kerry in Basel This Week
“Yes, I plan to,” Lavrov said told the news agency during his visit to the Sudanese capital.
Earlier on Tuesday, a Russian Foreign Ministry spokesperson said the meeting may take place on December 4-5.
According to the Russian Foreign Ministry, the diplomats also held "an intense exchange of opinions on the situation in Ukraine" and discussed the Minsk agreements on the sidelines of the Vienna talks.
Relations between Russia and the United States have deteriorated in the wake of the Ukrainian crisis, as Washington has accused Moscow of interfering in Ukraine"s internal affairs, claims repeatedly denied by the Russian side.