At 0743 GMT, the rouble was at 65.19 versus the dollar and stable at 73.07 against the euro .
Trading activity is below average between May 1-13 as the Moscow Exchange is closed on some of those days and many traders are away from their desks.
The finance ministry is in focus as it will announce details of its regular auctions of OFZ treasury bonds, due on Wednesday, after carrying out no auctions last week due to May holidays.
Demand for these bonds, which serves as a gauge of market sentiment toward Russian assets, has supported the rouble in the past few months.
Brent crude oil, a global benchmark for Russia's main export, was down 0.6 percent at $70.83 a barrel but, staying above the $70 threshold, remained supportive for Russian assets.
Russian stock indexes lacked momentum. The dollar-denominated RTS index was unchanged at 1,245.6 points, while the rouble-based MOEX Russian index slid 0.1 percent lower to 2,577.5 points.