The rouble was up 0.3pc at 62.80 against the dollar at 0731 GMT, heading away from the 63.12 it hit on Monday, its weakest level since Dec. 12, and trading at a long distance from an early January peak of 60.90.
Monday was the worst day for the rouble since August, Rosbank said in a note to clients.
"The coronavirus outbreak in China remains the main factor casting pressure on markets. But the most substantial reaction has already materialised on Monday," Otkritie Brokerage said.
When the panic fades, the rouble is likely to regain ground, supported by still high oil prices and the yields offered by rouble-denominated bonds, analysts say.
In the first half of 2020, the rouble's equilibrium rate is seen at 61-62 per U.S. dollar, according to Rosbank.
Versus the euro, the rouble was 0.4pc stronger at 69.10 but well off a 2020 peak of 67.65 seen some three weeks ago.
Russian stock indexes were up after a steep slide the day before, pricing in a stabilisation in oil. Brent crude futures , a global benchmark for Russia's main export, were down 0.1pc at $59.25 a barrel.
The dollar-denominated RTS index was up 1.0pc to 1,557.3 points. The rouble-based MOEX Russian index was 0.5pc higher at 3,101.3 points after falling on Monday to 3,076.68, its lowest level since Jan. 8.