Market activity on Monday is likely to be lower than usual due to a public holiday in the United States.
At 0739 GMT, the rouble was 0.2pc weaker against the dollar at 64.37, heading away from 64.0075, its strongest level since Sept. 25 hit on Friday.
The Russian currency, along with other emerging market peers, saw some support from positive expectations stemming from signs of progress in the Sino-U.S. trade standoff.
The rouble has more room to appreciate against the U.S. dollar, VTB Capital said in a note, citing its "quantitative USDRUB model."
The rouble should get support given current financial market fundamentals and ongoing inflows into the local debt market, VTB Capital said.
Inflows into Russian OFZ treasury bonds were spurred last week by intensified expectations that the central bank could cut its rate as soon as next week.
Versus the euro, the rouble was 0.1pc weaker at 70.94 .
Meanwhile, Russian stock indexes traced oil prices lower as Brent crude oil, a global benchmark for Russia's main export, shed 1.1pc to $59.83 a barrel.
The dollar-denominated RTS index was down 0.5pc to 1,323.2. The rouble-based MOEX Russian index was 0.2pc lower at 2,705.6.
Shares in Yandex rose 4.1pc to 1,977.0 roubles a day after plunging over 18pc as a media report renewed concerns over a draft law on limiting foreign voting power in the company.
Earlier this year, a lawmaker behind the idea on changes to Yandex's ownership told Reuters that the draft law was not aimed at making the company state-owned.