At 0713 GMT, the rouble was 0.1 percent weaker against the dollar at 66.10 and also eased 0.1 percent to trade at 75.54 versus the euro.
After the end of Russia's monthly tax payments earlier this month, which supported the rouble, the Russian currency in the past few days has been following its global peers that are now closely watching the US rate decision.
"The FOMC meeting is set to be the highlight of today's agenda," VTB Capital said in a note.
"This time, Fed Chair (Jerome) Powell will hold a press-conference after the meeting, but there will be no updates on the Fed's economic projections."
Weekly auctions of Russia's OFZ treasury bonds are also in focus as demand for these papers is a gauge of investors' sentiment towards Russia and concerns related to the possibility of fresh US sanctions on holdings of Russian state debt.
US President Donald Trump's administration on Sunday lifted sanctions on aluminium giant Rusal and other companies linked to oligarch Oleg Deripaska, defying a Democratic-led push in the US Congress to maintain the restrictions.
After outperforming the market on Monday, shares in Rusal then dropped and were down 4.6 percent on the day on Wednesday .
The benchmark MOEX index was 0.02 percent higher at 2,498.7 points, trading near its all-time high of 2,502.73 it briefly hit on Monday.
"The 2,500 mark serves as strong resistance for the MOEX index but the external positive mood this week might be not enough for it to break through it," Otkritie Brokerage said in a note.