Fresh foreign capital inflows also boosted the rupee value against the dollar, a forex dealer said.
The benchmark Sensex ended steady at 24,677.37 after moving in a wide range of 24,948.30 and 24,576.52.
The rupee resumed higher at 66.90 as against the yesterday's closing level of 67.22 per dollar at the Interbank Foreign Exchange market and firmed up further to 66.64 before ending at more than 2-month high at 66.75, showing a gain of 47 paise or 0.70 per cent.
The rupee has gained by 63 paise or 0.93 per cent in two days.
Weakness in the US dollar persisted during Asia trade today, briefly hitting a three-week low against the yen.
The dollar dropped swiftly and sharply against main rivals today after the Federal Reserve cut an old projection for US interest rate hikes to two from four for 2016, a move that initially spurred a risk-on rally throughout global equities and oil.
Pramit Brahmbhatt of Veracity Financial Services said,
"The rupee opened on a much stronger note, taking cues from FOMC statement (where Fed kept rate unchanged, leaving dovish stance) thus by weakening USD. This move will have a pressure on USD going forward. Positive sentiment in domestic equity market added fuel in rally of the rupee and helped the rupee to break resistance of 66.80/USD."
In forward market, premium for dollar dropped further due to persistent receivings from exporters.
The benchmark six-month premium for August dropped to 210-212 paise from 217-219 paise yesterday while far-forward February 2017 contract also closed lower at 414-416 paise from 423-425 paise.
The RBI fixed the reference rate for the dollar at 66.8806 and euro at 75.0735.
The domestic unit fell against the yen to settle at 59.97 per 100 yen from 59.24.
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