At 0713 GMT, the rouble was 0.2pc stronger against the dollar at 63.89 and had gained by 0.3pc to trade at 70.31 versus the euro.
"The Russian market appears stronger than other emerging markets on the backdrop of an increase in oil prices and ahead of tax payments of 1.1 to 1.4 trillion roubles," ING said in a note.
The rouble had reacted strongly to a surge in oil prices earlier this month in the wake of an attack on Saudi crude oil facilities, reaching its highest since July of 63.58 versus the dollar a week ago.
Oil prices rose more than 1pc on Monday on doubts over how fast Saudi Arabia can fully restore its crude output after the attack.
Brent crude oil, a global benchmark for Russia's main export, was up 0.8pc at $64.80 barrel at 0651 GMT.
Russian stock indexes were down.
The dollar-denominated RTS index was down 0.3pc to 1,373 points, while the rouble-based MOEX Russian index was 0.3pc lower at 2,787 points.