At 0720 GMT, the rouble was 0.2% weaker against the dollar at 62.8 and had lost 0.2% to trade at 70.7 versus the euro.
Markets are monitoring the prospect of a Fed rate cut and U.S. retail sales due to later on Tuesday that could serve as an indicator of U.S. economic health.
"For the entire group of EM currencies, and the Russian rouble in particular, the future monetary policy of leading central banks remains defining," Mikhail Poddubsky, an analyst at Promsvyazbank, wrote in a note.
The rouble was weighed down by oil prices that fell on Tuesday as output in the U.S. Gulf of Mexico resumed after Hurricane Barry.
Brent crude oil, a global benchmark for Russia's main export, was down 5 cents at $66.45 a barrel by 0749 GMT.
The dollar-denominated RTS index fell by 0.5% to 1,380 points, while the rouble-based MOEX Russian index was 0.1% lower at 2,752 points.
The Russian currency could later be buttressed by the finance ministry's weekly auction of OFZ treasury bonds scheduled on Wednesday. Investors tend to convert foreign currency into roubles to take part in the auctions.