However, persistent capital inflows from foreign funds restricted the rupee's fall, forex dealers said.
The local currency opened almost flat at 63.76 as against its previous closing of 63.77 at the Interbank Foreign Exchange (Forex) market. It moved in a range of 63.75 and 63.84 during the day before ending at 63.81, showing a loss of 4 paise or 0.06 per cent.
The domestic currency had lost seven paise, or 0.11 per cent, in last three days.
The US dollar index was trading higher by 0.02 per cent in late afternoon trade.
In Asian markets, the dollar struggled for direction with traders treading water as they waited for the top-tier non-farm pay-rolls report later in the day, which may strengthen or weaken the case for a September rate hike.
In New York, the dollar edged lower yesterday but finished just below over two week high against its main rivals.
Crude oil futures extended their slide yesterday as a persistent global supply glut, strengthening dollar and concerns over China's economy continued to put a bearish pall on the market.
Meanwhile, the benchmark BSE Sensex today ended lower by 61.74 points, or 0.22 per cent, at 28,236.39.
In the forward market, the premium for the dollar continued to fall on sustained receivings from exporters.
The benchmark six-month premium payable in January declined further to 209.5-211.5 paise from 211-213 paise yesterday and far-forward contracts maturing in July 2016 also fell further to 435.5-437.5 paise from 439-441 paise.
The RBI fixed the reference rate for the dollar at 63.8061 and for the euro at 69.6571.
The rupee fell against the pound sterling to close at 99.03 from 98.76 yesterday and also moved down against the euro to 69.76 from 69.50. The domestic unit dropped against the Japanese currency to 51.20 per 100 yen from 51.07 previously.
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