At 0723 GMT, the rouble was 0.1pc stronger against the dollar at 64.03 and added 0.1pc to 70.95 versus the euro.
"The rouble is likely to remain in a narrow range amid a neutral external backdrop," Nordea Bank analysts said in a note.
The Russian currency is likely to receive support from month-end tax payments, the bulk of which falls next week. Taxes usually prompt export-focused companies to convert part of their dollar and euro revenues to meet local liabilities.
Demand for Russian OFZ treasury bonds is also seen as supporting the rouble as investors buy into the Russian debt on expectations that the Russian central bank will cut rates by the end of this year, which should boost bond prices.
Brent crude oil, a global benchmark for Russia's main export, was down 0.8pc at $58.95 a barrel, limiting gains in Russian assets.
Russian stock indexes were up. The dollar-denominated RTS index rose 0.4pc to 1,353.0 points, while the rouble-based MOEX Russian index was 0.2pc higher at 2,750.4 points.
Shares in Russia's second-largest oil producer Lukoil outperformed the broader market by gaining 1.4pc after the company proposed paying an interim dividend of 192 roubles ($3.00) per share.