At 0755 GMT, the rouble was 0.6pc stronger against the dollar at 62.99 and had gained 0.7pc to trade at 68.73 versus the euro.
Brent crude oil, a global benchmark for Russia's main export, was up 2pc at $55.1 a barrel.
On Tuesday, China's foremost medical adviser on the coronavirus outbreak, Zhong Nanshan, said the numbers of new cases were falling in some provinces and the epidemic might peak this month.
"Global risk sentiment improved, as the daily rate of change in confirmed coronavirus cases continued slowing," said VTB Capital analysts in a note.
However, World Health Organisation chief Tedros Adhanom Ghebreyesus warned that the world must "wake up and consider this enemy virus as public-enemy number one", and the first vaccine was 18 months away.
On Tuesday, the finance ministry said it would tap into its National Wealth Fund to buy the central bank's $44 billion stake in Sberbank at market price, boosting the bank's stock. On Wednesday, Sberbank shares were flat.
ING Economics said the sale should lead to a decline in the central bank's foreign exchange purchases, which would help the rouble's exchange rate.
Russian stock indexes were up, also benefiting from hopes that coronavirus fears are easing.
The dollar-denominated RTS index was up 0.8pc to 1,552.5 points.
The rouble-based MOEX Russian index was 0.2pc higher at 3,103.8 points.
Gas giant Gazprom shares rose 1.8pc after a company official said on Tuesday its sales in Europe could be boosted by China taking the bulk of U.S. liquefied natural gas supplies.
The company's CFO said the Gazprom board would consider adjustments to its dividend policy in April.
The finance ministry will place two OFZ treasury bonds, which usually prompts foreign investors to buy roubles.
Yields on Russia's 10-year treasury bonds, which move inversely to their price, were at a one-month low of 6.15pc, after the central bank lowered its key rate to 6.00pc last week.