The local currency resumed weak at 63.45 a dollar from the previous close of 63.37 at the interbank foreign exchange market and dropped to a low of 63.46.
It bounced back to a high of 63.04 on firm local equities and slipped again on dollar demand from importers, mainly oil refiners, to end at 63.38, a fall of one paisa.
On May 16, the rupee closed one paisa higher at 54.77.
The Fed's decision on tapering its monthly $85 billion bond-buying programme is expected later on Wednesday.
The outcome of the two-day Fed meeting will be known after 2 pm EST in the US (about 11:30 pm Indian time).
"Rupee along with most asset classes are on a wait and see mode with US FOMC meeting slated tonight," said Anindya Banerjee, currency analyst at Kotak Securities.
"If the Fed does not change the language to dovish and does a taper of $10-15 billion, the rupee could come under pressure.
“A range of 61.50 to 64.50 could be seen over this week."
Local stocks ended higher at the fag end of a mostly flat session, with the benchmark S&P BSE Sensex up by 158.13 points or 0.8 per cent. Foreign institutional investors bought a net Rs 318.05 crore (Rs 3.18 billion) of shares on Tuesday, according to provisional data with the stock exchanges.
The dollar index was down 0.05 per cent against a basket of six major global rivals.
The markets are also awaiting the Reserve Bank of India's mid-quarter monetary policy review on September 20.