"We're not in the regime-change game. We are against interference in domestic conflicts," Lavrov told the BBC in an interview published Thursday. "It is not for us to decide who should lead Syria. It is for the Syrians to decide."
Since the conflict in Syria began two years ago this month, Russia has opposed international efforts to pressure Assad to step aside, insisting that Syrians should resolve the civil war, preferably politically.
Opposition groups have said Assad's ouster is a non-negotiable demand. However, Ahmed Moaz al-Khatib, leader of the National Coalition for Syrian Revolutionary and Opposition Forces, said in January the group was willing to consider the possibility of negotiations with the regime.
"I'm glad that the latest discussions and the latest gestures from the opposition, and statements from some of those who support the opposition, hint that they would be prepared to start negotiations with some negotiating team without asking President Assad to step down," Lavrov said Thursday.
Russia has been an ally of the Syrian government and is the country's largest arms supplier.
Lavrov is scheduled to visit London next week for talks with British Foreign Secretary William Hague.
Both countries said discussions will focus on the Syrian crisis.
Lavrov said he didn't think Britain and Russia differed that much on the goals for Syria, the BBC said.
"I don't think we are far apart as far as the eventual goal is concerned. We both want Syria to be united, to be democratic. We both want the Syrian people to choose freely the way they would like to run their country," Lavrov said. "That has been the Russian position ... since the crisis started."