Analysts said trading was quiet as the market waited for Friday's central bank board meeting, which will decide on rates and release details on how it will resume foreign currency purchases in January.
The central bank was last seen buying FX on the market in August. The question now is whether it will resume buying in full as budget rules require - which would hit the rouble - or whether it will just make some of the required purchases.
As of 0720 GMT, the rouble was 0.2 percent stronger against the dollar at 66.49, heading away from this month's low of 67.23 hit last week.
Versus the euro, the rouble was 0.1 percent stronger at 75.61.
A Reuters poll showed that the probability of the central bank keeping rates on hold was slightly higher than the chances of a rate hike.
"Activity among rouble players will be subdued ahead of the central bank meeting where issues of the rate level and a resumption of FX buying in accordance with the budget rule will be addressed," said Bogdan Zvarich, chief analyst at Promsvyazbank.
Brent crude oil, a global benchmark for Russia's main export, stabilised around $60 per barrel after days of elevated volatility boosted by talks about a global output cut deal.
OPEC and its Russia-led allies agreed last week to slash oil production by more than the market had expected despite pressure from U.S. President Donald Trump to reduce the price of crude.
Russian stock indexes were slightly down.
The dollar-denominated RTS index was 0.1 percent lower at 1,135.5 points, while the rouble-based MOEX Russian index was down 0.05 percent at 22,396.1 points.