At 0730 GMT, the rouble had gained 0.2pc to trade at 70.3 versus the globally weaker euro after briefly touching 70.25, a level last seen on March 22 last year.
Versus the US currency, the rouble was unchanged on the day at 63.15 per dollar.
"There are no sufficient reasons for strong moves (in the rouble vs the dollar) for now," Olma brokerage said in a note.
The rouble retains support from month-end tax payments that usually prompt export-focused companies to convert their dollar or euro revenues to meet local liabilities.
The rouble can return to a range of 62.8-63.0 versus the greenback on Wednesday thanks to demand from exporters, Rosbank analysts said in a note.
Companies are due to pay the mineral extraction tax by July 25, while the profit tax is due to be paid by July 29.
The Russian currency could receive support later in the day from the Finance Ministry's weekly auction of OFZ treasury bonds.
Earlier this year, investors used to convert foreign currency to take part in such auctions. But as foreign bidding in Russian treasury bonds eased recently, the rouble remains vulnerable to external pressure, VTB Capital analysts said.
Oil prices nudged higher on Wednesday on rising tensions over Iran, a sharp fall in US crude stocks and positive signs on China-US talks.
Brent crude oil, a global benchmark for Russia's main export, was up 0.2pc at $63.97 a barrel.
The dollar-denominated RTS index was flat at 1,345 points. The rouble-based MOEX Russian index was 0.15pc lower at 2,697 points.