By 0730 GMT, the rouble was 0.4pc stronger against the dollar at 63.33. Against the euro, the currency firmed 0.4pc to trade at 68.63.
China's central bank cut the interest rate on its medium-term lending to lessen the impact of the epidemic that has killed more than 1,700 people.
The move helped Chinese stock markets rally and buttressed other Asian bourses.
The rouble is also receiving a boost from the month-end tax period that began on Monday.
Tax payments generally prompt export-focused companies to convert foreign currency revenues to meet local liabilities.
Russian stock indexes were trading higher.
The dollar-denominated RTS index was up 0.7pc to 1,545.2 points, while the rouble-based MOEX Russian index was 0.3pc higher at 3,105.3 points.
Prices for Brent crude oil, a global benchmark for Russia's main export, were steady at $57.38 a barrel by 0722 GMT as expectations that output cuts from major oil producers offset concerns of falling fuel demand due to the virus epidemic.