The rouble lost about 8% last week and is down 12.5% this month after an oil embargo and price cap came into force. The finance ministry has said the recent decline was related to recovering imports.
At 0711 GMT the rouble was 0.8% stronger against the dollar at 69.67. It was up 2.3% against the euro at 73.91 and firmed 0.2% against the yuan to 9.91.
Trading activity is likely to be light on Monday, Otkritie Research said in a note, with the rouble able to strengthen in the continuing month-end tax period, which usually see Russian exporters convert foreign exchange revenue to pay local liabilities.
The rouble remains one of the world's best-performing major currencies against the dollar this year, supported by capital controls and reduced imports, but it has lost top spot to Brazil's real in the past week.
Brent crude oil, a global benchmark for Russia's main export, was up 3.7% at $84.0 a barrel, giving Russian equities some support.
Investors are likely to rebalance their portfolios in the final week of the year, which could move the market in either direction, Sinara Investment Bank said.
The dollar-denominated RTS index was up 0.1% at 964.1 points while the rouble-based MOEX Russian index gained 0.4% to 2,132.1 points.
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(Reporting by Alexander Marrow; Editing by David Goodman)
