As of 0738 GMT, the rouble shed 0.2 percent to 66.69 versus the dollar and was steady at 75.56 versus the euro .
"We're waiting for the oil decision ... But if the market doesn't like the scale of an oil output cut, oil can fall again below $60 per barrel and then we can move towards 68 (roubles per dollar)," said a dealer at a major Russian bank in Moscow.
The market expects the OPEC meeting in Vienna to result in a supply cut aimed at draining a glut that has pulled down crude by 30 percent since October. But OPEC is waiting to hear how much oil output Russia will cut before making its own decision.
Brent crude oil, a global benchmark for Russia's main export, was little changed on the day at $61.57 a barrel.
The room for the rouble's weakness, however, could be limited by higher interest rates at home that, in theory, increase the investment appeal of Russian assets.
Chances that the central bank will raise rates at its board meeting next week have increased after data showed on Wednesday that weekly inflation had recently picked up to 0.2 percent from 0.1 percent, Alfa Bank analysts said in a note.
A Reuters poll conducted in late November forecast that the central bank would need to raise rates in the next few months to tame rising inflation, given its plan to resume regular purchases of foreign currency on the local market from January.
Russian stocks indexes headed lower. The dollar-denominated RTS index was down 0.5 percent to 1,146.1 points. The rouble-based MOEX Russian index declined 0.7 percent to 2,429.2 points.