At 0739 GMT, the rouble was 0.2 percent weaker against the dollar at 65.72 and had lost 0.2 percent to trade at 74.67 versus the euro.
The Russian currency gained over 2 percent against the dollar on Friday, when U.S. data showed nonfarm payrolls increased last month by the fewest in more than 5-1/2-years.
That caused investors to rule out the chance of an interest rate hike by the U.S. Federal Reserve this month, boosting the appeal of higher-yielding emerging-market assets including those denominated in roubles.
The Russian currency was however supported by higher oil prices, which were helped on Monday by the weaker dollar and attacks on Nigerian oil infrastructure.
Brent crude oil, a global benchmark for Russia's main export, was up 1.2 percent at $50.2 a barrel.
Russian share indexes were higher on Monday, pricing in gains in oil prices after the market close in Moscow on Friday.
The dollar-denominated RTS index was up 1.4 percent to 914 points, while the rouble-based MICEX was 1.2 percent higher at 1,908 points.