The rouble was 0.1pc weaker against the dollar at 64.10 at 0753 GMT, close to the 64.19 two-week low hit on Thursday.
Against the euro, the rouble shed 0.1pc to 70.58 .
The Russian currency has come under pressure this week in the face of a continuing political stand-off between the United States and China, with Beijing reacting angrily to US President Donald Trump signing a law on Wednesday supporting protesters in Hong Kong.
The tensions increase investors' global risk aversion, exerting selling pressure on emerging market currencies.
The rouble also lost support from monthly tax duties paid earlier in the week, which usually prompt export-focused companies to convert part of their foreign revenues into the domestic currency.
However, the rouble remains the third best-performing currency against the dollar this year behind the Ukrainian hryvnia and Egyptian pound.
Russian shares were also down. The dollar-denominated RTS index dipped 0.2pc to 1,436 points and the rouble-based MOEX Russian index eased by 0.2pc to 2,2911.5 points.
Gazprom shares firmed by 0.1pc to 254.3 roubles ($3.98) after the company posted a 45pc drop in third-quarter net profit.