The White House said on Sunday that President Donald Trump was open to signing legislation toughening measures against Russia.
"The theme of sanction pressure from the United States is overwhelming again the minds of those who invest into Russian assets," Rosbank, a Russian subsidiary of Societe Generale, said in a research note.
The Kremlin expressed concerns that new sanctions could hurt major investment projects with European partners.
The rouble shed 1.1 percent to 59.98 against the dollar as of 1214 GMT. It weakened 0.9 percent to 69.84 against the euro, after briefly touching 70 versus the European currency, its lowest since mid-November.
The losses were capped by gains in oil prices. Brent crude oil futures, a global benchmark for Russia's main export, rose 0.7 percent to $48.4 a barrel after leading OPEC producer Saudi Arabia said it would cut exports to help correct market imbalances.
The Russian central bank could also prop up the rouble by supporting its high-yielding status, and analysts expect it resist pressure from business leaders for a steep cut in key interest rate from the current 9 percent at a board meeting on Friday.
Russian stocks dropped. The dollar-denominated RTS index shed 1.5 percent to 1,010 points, while the rouble-based MICEX was 0.1 percent lower at 1,922 points.