At 0745 GMT, the rouble was 0.23 percent stronger against the dollar at 64.21, having briefly touched 64.05 in early trading, a level not seen since March 26.
The Russian currency also gained 0.06 percent to trade at 72.66 versus the euro.
The rouble will be supported by the local tax payments and Russian assets may strengthen further if there is no significant news on global markets, analysts at Rosbank said in a note.
Tax payments, which begin on Monday and run until the end of the month, usually prompt export-focused companies to convert foreign currency to meet local liabilities.
"The dollar/rouble rate will probably try to break through the level of 64.0 during the week," the Rosbank analysts said.
Oil prices slipped but held near the previous session's five-month high.
Brent crude oil, a global benchmark for Russia's main export, was down 0.22 percent at $71.39 a barrel.
Russian stock indexes rose.
The dollar-denominated RTS index was up 0.45 percent at 1,259.04 points. The rouble-based MOEX Russian index was 0.27 percent higher at 2,566.44 points.