Medvedev, on the sidelines of a nuclear summit in South Korea, said he supports a joint U.N.-Arab League peace initiative offered by former U.N. Secretary-General Kofi Annan.
"We need to make sure that we not end up in greater problems than we already have, and that the threat of the civil war is averted, that it does not become reality, and that this mission would lead to dialogue between all the groups that exist in the country and government authorities," he said Monday.
Moscow has threatened to veto any formal action against Syria at the U.N. Security Council. U.S. President Barack Obama said alongside his Russian counterpart that while there were some differences, both sides agree on Annan's efforts.
A source identified by The New York Times as "an administration official" in the United States said Washington was supplying non-military aid to the rebel Free Syrian Army through an agreement with Turkey.
Thousands of people have died in the yearlong uprising against Syrian President Bashar Assad. U.N. officials have said Damascus should be brought before the International Criminal Court for war crimes though the Syrian government maintains its dealing with a domestic insurgency.
Human Rights Watch reported Monday that Syrian troops forced residents to march in front of advancing forces during recent operations.
"Somebody should be made to answer for these violations," Ole Solvang, emergencies researcher at Human Rights Watch, said in a statement.