Speaking at a news conference after meeting with his Palestinian counterpart Riyad al-Maliki, Lavrov confirmed Moscow's readiness to host a meeting between the Fatah and Hamas Palestinian factions, as well as a meeting of Israeli and Palestinian leaders.
He said Palestinian disunity is hindering the start of direct talks with Israel and urged all Palestinians to reconcile and give Ramallah the authority to negotiate.
For his part, al-Maliki accused Israeli Prime Minister Benjamin Netanyahu of "pretending" to be ready for a meeting with Palestinian leaders without preconditions, saying: "When it comes to the deal, Netanyahu somehow avoids it."
Commenting on the surprise U.S. announcement it will withdraw its troops from Syria, Lavrov said: “Any troop withdrawal is a step in the right direction".
The question is whether it will be implemented, he added, citing the U.S. withdrawal from Iraq and its later return, and frequent pledges to end its military presence in Afghanistan.
"I would prefer to see how this initiative will be implemented, what follows the announcement. As far as I heard, it provoked many questions even in the U.S., so let's wait for a clarification of the situation," he said.
Separately, Russian presidential spokesperson Dmitry Peskov said Moscow needs to understand the hows and whys of U.S. troops leaving Syria as well as what comes next.
In a surprise tweet on Wednesday, U.S. President Donald Trump declared victory over Daesh in Syria, saying its defeat was the sole reason for the U.S. presence in the country.
Reports have suggested the U.S. forces would leave within 60 to 100 days.
The U.S. began its air campaign in Syria in 2014, deploying troops to the country to assist in the anti-Daesh fight alongside local partners the year after.