At 0730 GMT, the rouble was 0.4% weaker against the dollar at 66.34 but still at a distance from a six-month low of 67.11 touched last week.
Versus the euro, the rouble lost 0.5% to trade at 73.69 .
The rouble eased despite prices for oil, Russia's main export, rising after U.S. President Donald Trump predicted a trade deal with China after positive comments by Beijing, calming nerves after a round of tit-for-tat tariff hikes.
China's yuan weakened for the ninth straight session on Tuesday, plumbing new 11-1/2-year lows.
Brent crude oil, a global benchmark for Russia's main export, was up 0.2% at $58.87 a barrel.
There are no explicit internal drivers to support the rouble, said Mikhail Poddubsky, an analyst at Promsvyazbank.
The peak tax period, which usually prompts companies to convert foreign revenues into roubles, ended on Monday. Some minor taxes are still due to be paid by the Russian companies this week.
The dollar-denominated RTS index was down 0.5% to 1,261 points. The rouble-based MOEX Russian index was 0.2% lower at 2,653 points.