The home currency largely withstood strong month-end demand for the American unit from importers despite extremely bullish sentiment for greenback overseas bolstered by good advance quarterly Q3 GDP print.
The rupee opened with a gap up at 64.88 against last weekend's close of 65.05 at the Interbank Foreign Exchange (FOREX) market due to easing dollar pressure.
Maintaining its strong edge, the local unit touched an intra-day high of 64.80 in last afternoon deals before ending at 64.85, showing a smart gain of 20 paise, or 31 per cent.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.9338 and for the euro at 75.4271.
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Trading has been thin and confined to extremely narrow range ahead of key global events with the US Federal Reserve announcing its monetary policy decisions followed by the highly anticipated US jobs report at the end of the week.
Persistent foreign capital inflows against the backdrop of domestic market's record-breaking performance also boosted the rupee value, a forex dealer said.
But, Fed interest rate decision is the key event to be watchful, he added.
In the meantime, global crude prices continued their bullish ascent with brent trading above the psychological USD 60-mark per barrel on expectations that an OPEC-led production cut due to expire next March would be extended.
On the global front, the dollar remained moderately lower against other major currencies after its biggest weekly rise this year as investors took profits before a central bank decision this week where markets are waiting to see if strong economic data will spur a more hawkish stance.
In cross-currency trades, the rupee fell back against the pound sterling to finish at 85.46 from 85.17 per pound and also retreated against the Japanese yen to close at 57.07 per 100 yens compared to 57.00 previously.
The local unit, however strengthened against the euro to settle at 75.43 from 75.54 last Friday.
Elsewhere, the euro is trading slightly higher against the US Dollar, correcting heavy losses from the second part of last week, though political trouble in Spain continued to weigh on the currency.
The benchmark six-month premium payable in March inched up to 115-117 paise from 114-116 paise and the far forward September 2018 contract moved up to 257-259 paise from 255-257 paise earlier.
On the International energy front, global crude prices continued their rallying momentum with strong compliance to OPEC's production curbs supporting prices, although rising exports from Iraq kept a lid on prices.
Brent crude futures, the international benchmark for oil prices, were at USD 60.73 per barrel in early Asian trade, up 29 cents or 0.48 percent above their last settlement.
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