Banks and importers preferred to increase their dollar position in view of higher greenback in the overseas market, forex dealers said.
Besides, fall in equity market affected the rupee value to some extent, they added.
The rupee resumed lower at 63.65 against previous closing of 63.58 at the Interbank Foreign Exchange (Forex) market and dropped further to 63.80 before finishing at more than 3-week low of 63.77, showing a loss of 19 paise, or 0.30 per cent.
The rupee had last ended at 63.84 on June 29, 2015. It has dropped by 22 paise, or 0.35 per cent, in last two days.
The local currency moved in a range of 63.63 and 63.80 per dollar during the day.
The dollar index, which tracks the greenback against a basket of major currencies, was down by 0.43 per cent. Oil prices were mixed in Asia in early trade, with WTI stuck below USD 50 a barrel after a rise in US stockpiles added to concerns over a supply glut, analysts said.
At the New York market, the dollar ended higher against most of its other rivals, after National Association of Realtors reported that US existing-home sales in June grew at the fastest pace since February, 2007.
Meanwhile, the benchmark BSE Sensex dropped by 134.09 points, or 0.47 per cent, to 28,370.84.
Veracity Group CEO Pramit Brahmbhatt said, "Rupee traded low for the day and depreciated by over quarter per cent, taking cues from local equities which traded low and closed on a weak note as subdued results from Lupin and Bajaj Auto, coupled with profit-booking in the market, forced rupee to decline."
The trading range for the Spot USD/INR pair is expected to be within 63.20 to 64.00. In the forward market, the premium for dollar ended lower on sustained receiving from exporters.
The benchmark six-month premium payable in December moved down further to 196-198 paise from 200-201 yesterday and far-forward contracts maturing in June, 2016 also declined to 425-427 paise from 428-430 paise. The RBI fixed the reference rate for the dollar at 63.7138 and for the euro at 69.6264.
The rupee fell further against the pound sterling to close at 99.54 from 99.41 yesterday and also dropped against the euro to 70.15 from 69.52 previously.
It also fell against the Japanese currency to end at 51.53 per 100 yen from 51.37 previously.
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