At 0746 GMT, the rouble was down 0.12% against the dollar at 64.54 and had lost 0.1% to trade at 72.18 versus the euro.
Brent crude oil, a global benchmark for Russia's main export, was down 0.29% at $69.91 a barrel.
The rouble received support from the tax period that began on Monday. Companies convert foreign revenue into roubles in order to pay mineral extraction tax and value added tax.
Andrei Kochetkov, an analyst at Oktritie Broker, said in a note that the rouble could strengthen until at least Wednesday when the Finance Ministry is due to hold its weekly auction of OFZ treasury bonds.
Rouble-denominated OFZ bonds, which serve as a gauge for global market sentiment, have drawn significant foreign demand in recent months.
"The real yield of the rouble remains one of the best in the world, which provides a stable demand for it in debt instruments," Kochetkov wrote.
Russian stock indexes were mainly flat.
The dollar-denominated RTS index was unchanged at 1,288 points. The rouble-based MOEX Russian index was 0.21% higher at 2,639 points.