A large uptick in foreign capital inflows along with unwinding of long-dollar positions by speculative traders predominantly supported the highly bullish upmove.
This is the highest closing since November 10, 2016.
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However, domestic equities couldn't find the magic as market players looked cautiously.
The home unit resumed firmly higher at 66.75 from last Thursday's closing value of 66.82 at the Interbank Foreign Exchange market and gained further ground to hit an intra-day high of 66.6450 before ending at 66.71, showing a rise of 11 paise, or 0.16 per cent.
Meanwhile, the US dollar traded little changed against its major counterparts.
The US dollar index was trading higher at 101.70 in the late afternoon session.
The RBI fixed the reference rate for the dollar at 66.7249 and for the euro at 70.5149.
In cross-currency trade, the rupee also rose sharply against the British pound to finish at 82.78 from 83.26 earlier.
But, the local currency weakened further against the euro to close at 70.56 as compared to 70.48 and also dropped against the Japanese Yen to settle at 59.42 per 100 yens from 58.97 previously.
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