At 0702 GMT the rouble was 0.3% stronger against the dollar at 64.81, and largely flat at 71.19 versus the euro.
Emerging market and commodity currencies strengthened in response to U.S.-China trade discussions.
Brent crude oil, a global benchmark for Russia's main export, rose 0.3% to $58.50 a barrel.
The dollar-denominated RTS index was down 0.08% to 1,319.14. The rouble-based MOEX Russian index was up 0.03% to 2,720.17.
"Today, the world currency market is calm, but there is a very weak trend to the weakening of the dollar," said Alexey Antonov from Moscow investment company ALOR Broker.
He added that the rouble may strengthen slightly today but "there are no reasons for stronger growth in the Russian currency yet."