At 0726 GMT, the rouble was 0.4 percent stronger against the dollar at 68.02, heading away from a low of 68.71 touched on Thursday, a level previously seen on Sept. 13.
The rouble took a hit this week from a drop in prices for oil, Russia's key export, as well as a global exodus from emerging market assets after the U.S. Federal Reserve raised its interest rates.
"Globally, the key driver of trading was the reverberation from the Fed meeting," VTB Capital analysts said in a note.
While trading activity is winding down ahead of Christmas holidays in Western markets and Russia's long New Year holidays, the rouble could still firm further thanks to local tax payments.
Russian tax payments usually prompt export-focused companies to convert their dollar and euro revenues.
"We believe the latter factor is likely to increase support for the rouble in the upcoming couple of sessions and help the rouble regain ground," VTB Capital said.
Versus the euro, the rouble was 0.5 percent stronger at 77.95, heading away from 78.89, its lowest level since mid-September briefly touched the day before.
On the stock market, shares in Rusal pulled back slightly after surging on Thursday after the United States said it would lift sanctions against the aluminium giant and its parent company EN+.
After soaring as high as 39 roubles per share on the Moscow Exchange on Thursday, Rusal shares were down 2.6 percent on the day at 29.67.
The dollar-denominated RTS index was up 0.3 percent at 1,086.8 points, while the rouble-based MOEX was 0.3 percent lower at 2,346.7 points.
"The Russian market is facing substantial global headwinds today, as global markets sink lower on a litany of issues from a weak global growth outlook, a slowing Chinese economy, trade tensions, higher U.S. borrowing costs, tumbling oil prices and on the near-term perspective, a potential U.S. government shutdown," Alfa Bank said in a research note.
Brent crude oil, a global benchmark for Russia's main export, was up 0.9 percent at $54.86 a barrel, having touched its lowest since September 2017 of $54.28 on Thursday.