"The Russian proposal on the resumption of direct negotiations between Belgrade and Pristina, which was earlier submitted to the UN Security Council, still stands," he told a news conference after a meeting with his Serbian counterpart, Vuk Jeremic.
Lavrov said a lasting solution to the Kosovo problem would only be able to be achieved if a consensus among all the parties concerned could be reached.
He also said Moscow intends to scrap visa requirements for Serbian citizens. Belgrade will follow suit.
"Today, we have discussed prospects for an agreement on a visa-free regime," he said.
Jeremic said Serbia is not against the presence of an EU civilian mission in Kosovo if it is approved by the UN Security Council.
He said Serbia does not intend to change its position on Kosovo.
"Serbia will not accept any decision violating its sovereignty, nor will it accept a decision that does not respect UN Security Council Resolution 1244 or a decision that is not based on negotiations and compromise," he said.
Kosovo, with a 90% ethnic-Albanian majority, has been formally recognized as a sovereign state by 43 UN member states, including the U.S. and most EU members since it proclaimed its independence from Serbia on February 17.
Russia, Serbia's long-time ally and a veto-wielding member of the UN Security Council, has refused to recognize Kosovo's independence.