At 0739 GMT, the rouble was 0.6pc stronger against the dollar at 63.74 and had gained 0.51pc to trade at 69.8 versus the euro.
The rouble touched its lowest against the dollar in more than two months on Friday after the central bank cuts its key interest rate for the sixth consecutive month.
"The rouble will try to strengthen, including thanks to speculators closing long positions (in safe assets)," said Alexey Antonov from the Alor Broker.
Rouble volatility has increased amid a global increase in risk aversion after the coronavirus outbreak in China.
"On the whole, the rouble's volatility in the coming days will still be very high. The range of fluctuations is still limited to 61.50-65.00 roubles to the dollar," said Antonov.
Brent crude oil, a global benchmark for Russia's main export, was down 0.18pc at $54.37 a barrel.
Russian stock indexes were mixed.
The dollar-denominated RTS index was up 0.72pc to 1,529 points. The rouble-based MOEX Russian index was 0.09pc higher at 3,090 points.