At 0751 GMT, the rouble gained 0.2 percent to 58.40 versus the dollar, its strongest since Nov. 7, and added 0.1 percent to 69.08 against the euro.
Trading activity on the Moscow Exchange was low as US market are closed on Thursday in observance of Thanksgiving Day.
Against the euro, the rouble lost 0.04 percent to trade at 69.19.
"The US markets are closed for the Thanksgiving Day, so the tone in the rouble is likely to be set by local players," analysts at VTB Capital said in a note.
The rouble usually enjoys support in the second half of every month as export-focused companies step up conversion of dollar revenues to meet local liabilities.
Earlier this week, the rouble could have seen support thanks to demand for the Russian currency from foreigners who took part in buying into yet another tranche of Russian treasury bonds, known as OFZs, offered by the finance ministry.
Brent crude oil, a global benchmark for Russia's main export, was down 0.4 percent at $63.05 a barrel, putting pressure on Russian stocks.
The dollar-denominated RTS index was down 0.1 percent at 1,157.7 points, while the rouble-based MICEX was 0.6 percent lower at 2,147.3 points.
Shares in Russian retailer Dixy Group outperformed, gaining more than 5 percent at the market opening after the company's board recommended shareholders to approve de-listing from Moscow Exchange at a price above the current market level.