At 0705 GMT, the rouble was 0.02 percent stronger against the dollar at 62.23 but eased 0.1 percent to 67.87 against the euro.
The rouble may see some support from the finance ministry which will offer up to 10 billion roubles ($160.67 million) in treasury bonds on Wednesday, Alpari brokerage said.
The Russian currency and rouble bonds are supported by the country's high yields thanks to the central bank's unwillingness to cut rates.
On the flip side, the rouble has lost local support from a monthly tax payment period as companies have already paid the bulk of their tax duties, analysts say.
Brent crude oil, a global benchmark for Russia's main export, was down 0.96 percent at $50.30 barrel, pressured by higher than expected increase in the U.S. inventories.
Lower oil prices put pressure on the stock market where the dollar-denominated RTS index lost 0.34 percent to 998.84 points, while the rouble-based MICEX was down 0.14 percent at 1974.49.