At 0809 GMT, the rouble was 0.14 percent weaker against the dollar at 57.58 and had lost 0.3 percent to trade at 70.95 versus the euro.
Oil fell by 2.4 percent on Monday, pressured by a rise in Russian production, expectations Saudi Arabia will cut prices of the crude it sends to Asia and a deepening trade spat between China and the United States.
In early Tuesday trade, Brent crude oil, a global benchmark for Russia's main export, was up 0.43 percent at $67.93 a barrel.
Russian stock indexes were down.
The dollar-denominated RTS index was down 0.41 percent at 1,229 points. The rouble-based MOEX Russian index was 0.45 percent lower at 2,247 points.
Global investors are worried about trade tensions between the United States and China. China imposed extra tariffs on 128 US products, deepening a dispute between the world's two biggest economies.
"Russia is somewhat immune to the global trade war that is brewing between the US and China," analysts at Alfa bank said in a note.
They also said the Russian market was supported by the recent recovery in oil prices and rumours President Putin could meet with President Trump in the United States.