There was little impact on the currency from a presidential vote which President Vladimir Putin won without any credible challenge on Sunday. The victory extends Putin's rule over the world's largest country for another six years at a time when his ties with the West are on a hostile trajectory.
At 0741 GMT, the rouble was 0.1 percent weaker against the dollar at 57.55 but had gained 0.1 percent to trade at 70.60 versus the euro.
The decline was limited by the support from the oil prices, which remain at around the highest level of this month. Brent crude oil, a global benchmark for Russia's main export, was down 0.32 percent at $66.00 a barrel after a strong growth on Friday.
The tax payments in Russia, which run to the end of the month, were also supporting the rouble.
The US Federal Reserve is in the market's sights as it is expected to lift its policy rate to a range of 1.5 to 1.75 percent at the end of its two-day meeting on Wednesday. The Russian central bank's rate decision follows on Friday.
Russian stock indexes, however, rose. The dollar-denominated RTS index was up 0.3 percent to 1,258.23 points. The rouble-based MOEX Russian index was 0.1 percent higher at 2,297.87 points.