Volatility on the Russian market has soared since Washington imposed fresh sanctions against Moscow on April 6, targeting major Russian companies and some of the country's most prominent businessmen.
Dangers of a direct military confrontation between Russia and the United States eased over the weekend after Western missiles fired at Syria over a suspected poison gas attack steered clear of any Russian troops on the ground.
But Washington said on Sunday it would impose further sanctions against Russia on Monday over Moscow's support for Syrian President Bashar al-Assad.
At 0740 GMT, the rouble was 0.36 percent weaker against the dollar at 62.27 and had lost 0.37 percent to trade at 76.80 versus the euro.
Russia's dollar-denominated RTS index was down 0.57 percent to 1,098.26 points, while the rouble-based MOEX Russian index was 0.18 percent lower at 2,171.28 points.
Shares in aluminium giant Rusal, which was placed on the April 6 US sanctions list, were down more than 5 percent on the Moscow Exchange after falling 30 percent in Hong Kong.
"Fears of a direct military conflict between the US and Russia have been sidelined, allowing markets to breathe easier, but only somewhat," BCS analysts said in a note.
"Sentiment, still, will be tempered awaiting the Kremlin's response to the US-led strike in Syria, to US sanctions of last week and potential new sanctions."
Lower prices for oil, Russia's main export, also weighed on Russian assets.
Benchmark Brent crude oil was down 1.58 percent at $71.43 a barrel as a rise in US drilling for new production weighed on prices.