The visit by the Syrian Negotiations Commission (SNC) comes as Moscow gets set to host peace talks in the Black Sea resort of Sochi on January 30 along with Syrian regime backer Iran and rebel supporter Turkey.
The SNC has said it will attend fresh UN-hosted negotiations before then but has not yet announced if it will also go to the Sochi talks, which dozens of rebel factions have already rejected.
A statement by the SNC said today's visit was "in response to an invitation by the Russian foreign ministry" and that its delegation will hold talks with the foreign and defence ministers as well as members of parliament.
SNC spokesman Yahya al-Aridi told AFP the opposition wanted "simply to make sure that Russia is serious about the entire peace process", particularly UN-led talks.
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Numerous rounds of UN-brokered peace talks have been held in Geneva, and the last one concluded in mid-December with no notable progress towards ending the country's war.
They are to resume January 25-26, this time in Vienna, ahead of the Sochi talks.
The Sochi meeting is now part of a broader push by Moscow to start hammering out a path to a political solution to end the war and has sparked concerns that the Kremlin is looking to sideline the UN.
The Damascus government has said it would attend the Sochi talks, which are aimed at setting up a new constitution for post-war Syria.
Syria's nearly seven-year war, which began as the regime brutally crushed anti-government protests, has claimed more than 340,000 lives, forced millions to flee their homes and left the country in ruins.