The rouble opened 0.3 percent stronger at 67.27 versus the dollar as of 0712 GMT, heading away from the previous day's 67.80 which was its weakest since Nov. 14.
The U.S. Treasury said it would lift sanctions on the core empire of Russian businessman Oleg Deripaska, including Rusal and EN+, watering down the toughest penalties imposed since Moscow's 2014 annexation of Crimea.
Rusal Moscow-listed shares jumped to 39.00 roubles at the market opening, a level last seen in early March, before paring gains to 31.75 roubles, up 20.5 percent on the day.
"The planned removal of Rusal and EN+ from the SDN sanctions list should provide Russia with a relief rally today, despite the gloomy backdrop on external markets after last night's Fed meeting," Alfa Bank analysts said in a research note.
The U.S. Fed raised interest rates again on Wednesday despite calls to the contrary from President Donald Trump and after weeks of market volatility. It also stuck by its plan to keep withdrawing support from an economy it views as strong.
Russian markets are also bracing for an annual news conference by President Vladimir Putin on Thursday. This usually goes on for several hours and touches upon various topics from geopolitics to domestic grain harvest.
Brent crude oil, a global benchmark for Russia's main export, played on the downside for Russian assets as it slipped 1.6 percent lower to $56.30 per barrel.
Stock indexes tracked oil prices lower, with the dollar-denominated RTS index falling 0.8 percent to 1,091.2 points and its rouble-based peer MOEX shedding 1.2 percent to 2,331.2 points.