At 0740 GMT, the rouble was 0.3 percent stronger against the dollar at 62.18 and had gained 0.3 percent to trade at 67.69 versus the euro.
The rouble is still supported by monthly tax payments that prompt export-focused companies to convert dollars and euros in order to meet local liabilities.
Oil prices also played on the upside for Russian assets as Brent crude oil, a global benchmark for the country's main export, was up 0.1 percent to $51.82 a barrel.
Gains in oil prices are likely to be restrained by concerns that global oil producers won't agree on capping output. Iraq already said it should be exempt from OPEC crude output restrictions.
Following an increase on Asian stock markets, the dollar-denominated RTS index gained 0.9 percent to 995.33 points, while the rouble-based MICEX grew 0.3 percent to 1963.36 points.