At 0803 GMT, the rouble was 0.2pc stronger against the dollar at 63.14, having stepped away from its weakest level since Dec. 11 of 63.51 it briefly touched on Thursday.
Against the euro, the rouble was 0.3pc stronger at 69.64 after hitting 70.07 on Thursday, a level last seen in mid-December.
The outbreak of the coronavirus remains in focus as its death toll topped 200 and the World Health Organisation (WHO) declared a global health emergency, boosting concerns about the economic implications.
Russia kept its lengthy land border with China partially closed to try to prevent the coronavirus spreading from its southern neighbour and suspended the issuance of electronic visas to Chinese nationals.
"The rouble volatility has increased amid this backdrop, but its weakening is not threatening as the rouble just got back to levels of December 2019," Rosbank said in a note.
"We still expect the rouble rate to stabilise in the range of 61.5-62.5 (versus the dollar) on a one-month horizon."
Oil prices rose on Friday following sharp losses this week, with Brent crude oil, a global benchmark for Russia's main export, gaining 1.1pc to $58.91 a barrel.
Tracking moves in oil prices, the dollar-denominated RTS index was up 1.2pc to 1,562.5 points.
The rouble-based MOEX Russian index was 0.8pc higher at 3,131.9 points.
Russian oil producer Lukoil outperformed the broader market by gaining 3.2pc on the day after global index provider MSCI increased the weight of Lukoil shares in its indexes.