Persistent foreign capital inflows also boosted the rupee value against the dollar to some extent, a forex dealer said.
The rupee resumed higher by 66.48 against yesterday's level of 66.52 per dollar at the Interbank Foreign Exchange market and hovered in a range of 66.5650 and 66.28 per dollar before finishing at 66.33, showing a gain of 19 paise or 0.29 per cent.
The rupee dropped to 66.5650 during the intra-day trade on month-end dollar demand from importers, mainly oil refiners.
The dollar index was down by 0.43 per cent against a basket of six currencies in the late afternoon trade.
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At the overseas, the US dollar were mostly lower against the basket currencies, while the yen surged to an 18-month high against the dollar in early trade, staying firm in the wake of the Bank of Japan's decision the previous day to hold off from expanding monetary stimulus.
The RBI fixed the reference rate for the dollar at 66.5176 and euro at 75.7303.
In cross-currency trades, the rupee dropped against the pound sterling to finish at 97.05 from 96.79 yesterday.
In overseas market, the dollar tumbled against the yen in
the late afternoon trade, as the continued surge for the Japanese currency triggered shock waves first in Asian currency markets and then deeper into Friday's trading session.
As part of that turbulence, the Chinese yuan was fixed at more than half a per cent higher, its biggest daily increase in more than a decade.
The yen hit an 18-month high against the dollar even with markets in Japan closed for a national holiday, as the currency builds on Thursday's 3.3 per cent gain registered after the Bank of Japan disappointed investors.
In forward market, premium for dollar eased further on sustained receivings from exporters.
The benchmark six-month premium for September eased to 179-181 paise from 180-182 yesterday and far forward March 2017 contract also moved down further to 368.5-370.5 paise from 370-372 paise.
Meanwhile, the benchmark Sensex ended steady at 25,606.62.