Consistent unwinding by foreign investors on worries regarding the controversial tax issues as well as renewed possibility of the Federal Reserve raising US interest rates predominantly kept home currency under intense pressure.
Month-end dollar demand from oil companies, along with aggressive hedging strategy adopted by importers in the wake of currency volatility, also weighed on the rupee trade.
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But, it recovered immediately to trade briefly at a fresh intra-day high of 67.5975.
However, the rupee suffered a late-morning blow and witnessed a sharp downturn to hit a low of 67.77 before concluding at 67.75, revealing a fall of 26 paise, or 0.39 per cent - extending its longest losing streak since 2007.
Meanwhile, the RBI fixed the reference rate for the dollar at 67.7060 and euro at 75.9323.
In cross-currency trades, the rupee retreated sharply against the pound sterling to finish at 98.98 from 97.71 on Monday. The local unit continued to slide against the euro and settle at 75.73 compared to 75.66 and dropped further against the yen to close at 61.80 per 100 yens against 61.69 earlier.
On the global front, the dollar continued to trade higher against other major currencies on expectations that the Fed will raise interest rates at the June meeting amid robust US macro outcome.
The dollar index, which tracks the world's reserve currency against a basket of its peers, is firmly higher by 0.13 per cent at 95.36.
In forward market, premium for dollar continued to fall on sustained receivings from exporters.
The benchmark six-month premium for October moved down to 179-181 paise from 180-182 paise and far forward April 2017 contract also softened to 377-379 paise compared to 378-380 paise earlier.
Meanwhile, Indian markets staged a modest rebound after four-straight day fall with the flagship index Sensex gaining 75.11 points to end at 25,305.47 and broader Nifty up by 17.80 points to settle at 7,748.85.
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