At 0730 GMT, the rouble was 0.03% stronger against the dollar at 64.46 and had gained 0.1% to trade at 72.18 versus the euro.
Oil prices were under pressure from Sino-American trade tensions but supported by OPEC's supply cuts. Brent crude oil , a global benchmark for Russia's main export, was up 0.01% at $68.70 a barrel.
The risks associated with the trade tensions between the U.S. and China persist for global markets despite the absence of specific deadlines for the negotiations, analysts at Rosbank said in a note.
"Obvious triggers for increased volatility in the rouble are not yet visible," Mikhail Poddubsky, an analyst at Promsvyazbank, wrote in a note. "We expect the consolidation of the dollar/rouble pair to continue near current levels."
The rouble was also bolstered by month-end tax payments ending on Tuesday. These payments usually prompt export-focused companies to sell foreign currency to meet liabilities at home.
Russian stock indexes were up.
The dollar-denominated RTS index was up 0.2% to 1,281.61 points, while the rouble-based MOEX Russian index was 0.11% higher at 2,622.23 points.