Russia's preparations to retaliate to US sanctions have added to the market uncertainty. The lower house of parliament is considering making it a crime to comply with sanctions imposed by the United States or other countries.
The rouble was little changed at 61.75 versus the dollar as of 0750 GMT and eased 0.2 percent to 73.01 against the euro.
Contemplating risks of more sanctions against Russia and Moscow's possible retaliation, market players are not rushing to buy into the rouble, which looks undervalued given current prices for oil, Russia's key export.
Brent crude futures rose 0.3 percent to $79.50 per barrel, its highest since November 2014. When oil prices last hovered at current levels, the rouble traded at 48 per dollar.
The Russian stock market also showed muted reaction to higher oil prices. The rouble-traded MOEX index was unchanged at 2,338.2, while its dollar-traded peer RTS climbed 0.2 percent higher to 1,192.2.
Shares in Russian mobile operator Megafon went down 0.4 pct, underperforming the broader market after the company's board recommended to pay no dividends for the 2017 financial year.