The rouble was little changed at 65.55 versus the dollar at 0716 GMT and eased 0.1 percent to 74.38 against the euro.
Month-end tax payments provided the main support for the rouble, analysts at Rosbank said in a note.
Tax payments usually prompt export-focused companies to convert their foreign currency revenues to meet local liabilities in the second half of every month.
In the near term, the rouble is likely to stabilise within a range of 65.50-66.00 against the dollar, Olma brokerage said.
Prices for oil were supportive for Russian assets. Brent crude oil was up 0.1 percent at $67.16 a barrel, trading near its highest level so far this year of $67.38 hit earlier this week.
The dollar-denominated RTS index was unchanged at 1,188.65 points, while the rouble-based MOEX Russian index was 0.1 percent higher at 2,471.9 points.