The possibility of demilitarizing this conflict was brought up in Geneva, and Moscow would like to understand how it can be done as weapons deliveries to the Syrian opposition continue, Lavrov said.
Russia also would like to receive an explanation how the opposition's certain supply routes will be checked, the minister said.
If Russia were given such an answer, it could consider some steps to demilitarize the conflict in Syria, he said.
The US backs the embargo on weapons supplies to Syria, US Ambassador to Russia Michael McFaul said on Ekho Moskvy radio on Thursday.
McFaul also confirmed that it is the U.S. position that Syrian President Bashar Assad should resign.
Russia and the United States stand for an immediate end to the bloodshed in Syria.
According to the Russian Foreign Ministry, The Russian President’s special envoy to the Middle East, Mikhail Bogdanov, and the US Deputy Secretary of State, William Burns, reiterated, during their recent meeting, their mutual adherence to the Final Communiqué, agreed by the Action Group for Syria in Geneva on June 30th 2012.
The two diplomats stressed the need for an immediate initiation of a transition political process to launch dialogue between the warring Syrian sides.
The Russian and American diplomats met yesterday on the sidelines of the fifth ministerial meeting of the Friends of Yemen Group in London.
Russian Foreign Minister Sergei Lavrov and US Secretary of State John Kerry had a telephone conversation on Saturday at the initiative of the American side, the Russian Foreign Ministry reports.
"The situation in Syria, the Middle East settlement agenda, and also certain topical issues in bilateral relations, including the state of Russian children adopted to the United States were discussed," the report says.
Voice of Russia, Interfax, MID.ru