Kurdish leader of the umbrella organisation Syrian National Council (SNC) based in Turkey and openly backed by Western and Arab states.
Russia has seen itself cast as the last protector of an Arab ally it buttressed in the Soviet era and has in the past year rejected two rounds of UN Security Council sanctions as well as calls for the use of force.
But Moscow is increasingly keen to be viewed as a nation crusading for the supremacy of international principles and self-determination rather than the global rule of powers such as the United States.
On Tuesday Moscow proposed a UN Security Council resolution on Syria that would extend the UN mission in the conflict-stricken country without any threat of sanctions, diplomats said.
The resolution was sent to the council's other 14 members ahead of a briefing on Wednesday by UN-Arab League envoy Kofi Annan on efforts to revive his peace plan, Russia's deputy UN envoy Igor Pankin told reporters.
Russia's move is the opening round in a potentially tense diplomatic battle at the Security Council that must decide the future of the UN observer mission in Syria by July 20.
Russia is the main ally of President Bashar al-Assad and has fiercely resisted international action against the Damascus government. The United States and European powers want sanctions against Assad over the conflict, in which activists say more than 17,000 people have died.
Russia has repeatedly said that the fate of Assad is up to the Syrian people and has defied calls by the West and the SNC to urge the Syrian president to step down.
"We are not holding on to specific personalities. This is not even an issue for us," Deputy Foreign Minister Mikhail Bogdanov said on the eve of the visit.
Bogdanov added: "We try to move the Syrian opposition figures toward realistic and constructive positions that can help end the bloodshed."
The SNC meanwhile signalled it may try to use the gentle art of persuasion rather than present Russia's top diplomats with a laundry list of complaints that have accumulated since fighting first flared in March 2011.
"We hope that they will try to understand and help us," said SNC spokeswoman Bassma Kodmani.
"Russia is one of the most important states for Syria. It plays an important role that we hope can help us turn the page on the old regime."
The soft tone masks outrage among SNC members and various states at Russia's decision to continue supplying Assad with military hardware even as the death toll surpasses 17,000 lives.
Russia says the arms can only help protect Syria's borders and are perfectly legal. It has also pledged not to send any of its latest technology even as it continues to fulfill orders placed by Assad before the crisis began.
But the SNC is expected to use the same argument used on Russia by rebels who came to Moscow for talks from Libya one year ago -- that regimes fall and new forces that replace them remember their foreign friends in times of need.
"We want to explain that the dictatorial regime that ruled Syria for more than 40 years has reached its end," Sayda said this week.
Moscow will be particularly keen to look after its lone naval port outside the ex-Soviet Union -- a centre in Tartus that lets Russia patrol the volatile region's shores -- as well as numerous commercial and diplomatic contacts.
The SNC talks come two days after Moscow received the more moderate Syrian intellectual and opposition member Michel Kilo in what has emerged as one of its most active burst of contacts with Assad's formal enemies.
Kilo said he had told the Russians that he could no longer support holding a dialogue with Assad because the fighting had gone too far.