Massive inflows of foreign funds into equities and debt further bolstered the forex sentiment.
The home currency though witnessed tight range-bound trade and moved between 63.61 and 63.73 most part of the day.
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It accelerated further to hit a high of 63.61 in mid-morning deals but traded stubbornly narrow-range before concluding the day at 63.69, revealing a good gain of 9 paise, or 0.14 per cent.
The RBI, meanwhile fixed the reference rate for the dollar at 63.6439 and for the euro at 78.4538.
Foreign investors are seemed to be interested in the Indian capital markets in a big way as they infused a whopping Rs 87 billion (Rs 8,700 crore) this month so far on expectations of better corporate earnings.
Highly positive global currency momentum with the reopening of the US government and the Bank of Japan seemingly talking down the prospect of an end to the stimulus it provides for the Japanese economy both helping to boost confidence.
Meanwhile, the greenback remained heavily offered across the board driven by fears that US President Trump may be sparking a new round of trade wars following the latest protectionist measures.
On the international commodity front, crude prices traded near three-year highs, though gains were capped due to a modest rise in US crude and gasoline inventories.
Brent crude futures were trading higher at USD 69.85 a barrel in early Asian trading.
In the meantime, the bull run on Indian bourses continued unabated for the sixth consecutive session with both the key indices hitting new historic peaks following strong buying momentum driven by encouraging earnings from blue-chip companies amid optimism in the global economy.
The benchmark BSE Sensex rose 22 points to end at 36,161.64, while Nifty added 2.30 points to 11,086.
On the global front, the greenback extended losses to hit a fresh three-year trough against other major currencies.
It hit a four-month low against the Japanese Yen on growing concerns that central banks other than the Federal Reserve will in due course start to unwind their own post- crisis stimulus.
The dollar index, which measures the greenback's value against a basket of six major currencies, was up at 89.44 in early trade.
In cross-currency trades, the rupee remained weak against the pound sterling and finished at 89.87 per pound from 88.95 and drifted further against the Japanese yen to settle at 58.18 per 100 yens from 57.77 yesterday.
The home unit also fell back after a brief recovery against the euro to end at 78.58 from 78.10 earlier.
Elsewhere, the pound sterling surged to hit a fresh 18-month high on the back of better-than-expected UK jobs data along with wages rising in line with expectations despite IMF downgrading the outlook for the UK growth.
The common currency euro climbed to 3-year high against the American dollar boosted by robust macroeconomic indicators.
In forward market today, premium for dollar continued move down on sustained receiving from exporters.
The benchmark six-month forward premium payable in June edged down o 119-121 paise from 121-123 paise and the far-forward December 2018 contract also eased to 256-258 paise from 257.50-259.50 paise previously.
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