The rupee moved in a tight range for much of the session.
The Fed is expected to announce the end of its bond-buying programme but also signal caution about the timing of any hikes in US interest rates.
Some analysts said the Fed's stance may have already been priced into the rupee's movement. The rupee has gained around 0.69 percent so far this month against the dollar after inflows continued into the debt markets despite mild selling in shares.
"FOMC will be dovish, which is already priced into the market, so I expect EM currencies to weaken after the FOMC statement," said Hemal Doshi, a currency strategist at Geojit Comtrade Ltd.
The partially convertible rupee closed at 61.35/36 per dollar, slightly weaker from its close of 61.32/33 on Tuesday.
The rupee had weakened slightly in intraday trade after some banks purchased dollars to meet month-end demand from importers, traders said.
But the currency received support as Indian stocks gained for a second straight session to their highest closing level in five weeks.
In the offshore non-deliverable forwards, the one-month contract was at 61.56/66, while the three-month contract was at 62.16/26.
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