At 0747 GMT, the rouble was 0.2pc stronger against the dollar at 64.01, pulling away from Monday's 10-week low, and had gained 0.2pc to trade at 69.86 versus the euro.
Brent crude oil, a global benchmark for Russia's main export, was up 0.8pc at $53.7 a barrel.
On Monday, Chinese authorities reported a daily drop in the number of new cases of coronavirus for just the second time in two weeks, while only 319 cases have been confirmed outside mainland China.
However, worry grew on Tuesday that the extent of economic disruption from the outbreak was being underestimated as the China's death toll from the epidemic soared past 1,000.
"Investors remain focused on coronavirus headlines," VTB Capital analysts said in a note.
Markets fear a possible slowdown in Chinese gross domestic product growth, which could affect its demand for raw materials and hamper global supply chains.
Also attracting market focus on Tuesday is U.S. Federal Reserve Chair Jerome Powell, who is expected to sound fairly upbeat about the outlook for U.S. economic growth when he testifies on Tuesday and Wednesday in Congress, despite the Fed's current policy being criticised by President Donald Trump.
"Powell's speeches in the House and Senate today and tomorrow are in the centre of attention after Trump's criticism," Rosbank analysts said in a note.
Russian stock indexes were up, after falling to five-week lows on Monday.
The dollar-denominated RTS index was up 0.8pc to 1,515.7 points.
The rouble-based MOEX Russian index was 0.5pc higher at 3,079.3 points.