At 0740 GMT, the rouble was 0.2 percent stronger against the dollar at 66.56 and had gained 0.1 percent versus the euro to trade at 74.15.
Brent crude oil was down by 0.9 percent on Wednesday to $49.4 a barrel as production from major Middle East exporters was expected to stay high.
Oil prices are still close to their highest this year, supporting the rouble as the commodity is Russia's main export.
Oil's recovery from multi-year lows around $27 a barrel in mid-January has helped lift the rouble by over 20 percent against the dollar since that point.
Analysts say the rouble will probably continue to track oil prices but that a potential interest rate rise by the U.S. Federal Reserve could apply downward pressure.
Market attention this week will be focused on the outcome of an OPEC meeting in Vienna, although few in the market expect the producer group to agree a united strategy to support prices.
Russian share indexes were mixed on Wednesday.
The dollar-denominated RTS index was down 0.4 percent to 900 points, pricing in the falls in the rouble and oil late on Tuesday. The rouble-based MICEX was 0.2 percent higher at 1,903 points.