At 0720 GMT, the rouble was 0.1% stronger against the dollar at 64.64, moving away from its lowest level since Sept. 12 of 64.71, which it touched on Friday.
The rouble is likely to trade within a range of 64.25-64.75 against the dollar on Monday, said Dmitry Polevoy, chief economist at Russian Direct Investment Fund.
Versus the euro, the rouble gained 0.1% to trade at 70.7 .
The Russian market has no strong internal drivers at the moment and external factors will continue playing the key role, said Mikhail Poddubsky, an analyst at Promsvyazbank.
On Monday, the rouble may get some support from the need to pay the last monthly tax, the income tax. Tax payments usually prompt companies to convert their foreign currency holdings to meet local duties.
The rouble's gains versus the dollar were limited as global political uncertainty and fears over a widening of the Sino-U.S trade war kept investors in safe harbours.
Market activity this week is likely to be below average as Chinese markets will be closed for public holidays for one week starting from Tuesday.
Prices for oil, Russia's main export, slipped as China's economic outlook remained weak even as manufacturing data improved.
Brent crude oil was down 0.5% at $61.61 a barrel.
The dollar-denominated RTS index was down 0.4% to 1,342 points. The rouble-based MOEX Russian index was 0.2% lower at 2,753 points.