At 0740 GMT, the rouble was 0.4% stronger against the dollar at 65.97, up from the 67.14 it had touched earlier this week, its lowest since Feb. 14.
Versus the euro, the rouble had gained 0.3% to trade at 72.82, its strongest since Aug. 23.
The rouble and other emerging-market currencies gained ground as China and the United States agreed to hold trade talks in early October, easing fears that an escalating trade war would trigger a global recession.
The rouble also enjoyed support from buyers of Russian OFZ treasury bonds, who were expected to snap up bonds before the central bank's rate-setting meeting on Friday.
Investors expect the central bank to cut its benchmark interest rate by 25 basis points to 7.0% on Friday.
This week, demand was strong for OFZ bonds, a gauge of investor sentiment towards Russian assets. Demand exceeded the amount of OFZ bonds on offer by three-fold at the finance ministry's weekly auction on Wednesday.
That has pushed yields of 10-year OFZ bonds to 7%, their lowest since March 2018. Bond yields move inversely with their prices.
"Confidence in the rate cut is growing," Freedom Finance brokerage said.
Russian stock indexes edged up. The dollar-denominated RTS index was up 0.5% to 1,338 points. The rouble-based MOEX Russian index was 0.4% higher at 2,803 points.
Shares in Surgutneftegaz fell 5% after its chief executive, Vladimir Bogdanov, said the recent spike in shares was caused by speculative trading.