At 0752 GMT, the rouble was 0.2% weaker against the dollar at 62.92 and had lost 0.1% to trade at 70.85 versus the euro.
Nordea Bank analysts said they expected the rouble to remain in a range of 62.5-63.5 to the dollar at least until the outcome of the U.S. Fed meeting on July 31, at which it is widely expected to trim rates.
The market sees a 56.5% probability of a 25 basis point cut and a 43.5% probability that rates will be cut by 50 basis points.
Fed Vice Chair Richard Clarida said on Thursday that U.S. policymakers might need to act early to stimulate the U.S. economy.
The benchmark price for oil, Russia's key export, hit a one-month low late on Thursday amid a sell-off on the U.S. stock market but pared losses on Friday.
Brent crude oil was up 1.2% on Friday at $62.66 a barrel.
Russian stock indexes rose. The dollar-denominated RTS index was up 1.1% to 1,365 points. The rouble-based MOEX Russian index was 0.8% higher at 2,724 points.
Shares in Norilsk Nickel, the world's largest palladium and refined nickel producer, rose 2% to a record high of 15,084 roubles ($239.85).
Aton brokerage, upgrading Norilsk's shares to "outperform", said that, even at current highs, they remained cheap.
"Russia is highly attractive and Nornickel is likely to be the first company in the metals and mining sector to receive international inflows, we believe," Aton said.