At 0703 GMT, the rouble was 0.08 percent stronger against the dollar at 66.50 and had gained 0.15 percent to trade at 76.35 versus the euro.
Brent crude oil was up 0.74 percent at $84.53 a barrel.
The finance ministry is due to decide whether to sell OFZ bonds this week. It has scrapped recent weekly auctions, in which it borrows by selling OFZ bonds on the market, in order to reduce volatility following an exodus of foreign investors.
Russian stock indexes were also on the rise.
The dollar-denominated RTS index was up 0.90 percent to 1,169.6 points. The rouble-based MOEX Russian index was 0.55 percent higher at 2,467.5 points.