At 0752 GMT, the rouble was up 0.3pc against the dollar at 63.43 and had also gained 0.3pc to trade at 68.76 versus the euro.
The daily death toll in Hubei, the Chinese province where the coronavirus outbreak began, halved and the number of new cases dropped from a record posted the day before.
"The external background in the morning can be called neutral," said Alexei Antonov, an analyst at Alor Brokerage, adding that uncertainty was still a factor.
Market sentiment also improved after a World Health Organization official said the big jump in China's reported cases reflects a decision by authorities there to reclassify a backlog of suspected cases by using patients' chest images, and was not necessarily the "tip of an iceberg" of a wider epidemic.
"The WHO has moderately lifted risk appetite, indicating the higher readings from the new diagnostic methodology did not necessarily indicate a spike in 'C'-virus cases," BCS Global Markets analysts said in a note.
Markets will closely follow the rouble's progress in the coming months after Finance Minister Anton Siluanov said on Thursday that Russia will pay a first instalment of 1.2 trillion roubles ($18.9 billion) for the central bank's stake in Sberbank in the spring.
Brent crude oil, a global benchmark for Russia's main export, was up 0.1pc at $56.4 a barrel.
Russian stock indexes were up. The dollar-denominated RTS index was up 0.3pc to 1,548.4 points. The rouble-based MOEX Russian index was 0.2pc higher at 3,117.3 points.