This is the highest closing for the home currency since August 8 last year when it had settled at 63.63.
Continuing its winning streak, the rupee has strengthened by a solid 47 paise in last three sessions.
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Expectations of robust capital inflows into the country on the back of relevant economic policy measures also kept forex market undertone highly buoyant.
In the meantime, India's foreign exchange reserves surged by USD 3.53 billion to touch a new life-time high of USD 404.921 billion in the week to December 22, aided by an increase in foreign currency assets, RBI data showed.
The rupee had risen almost 6 per cent against the US dollar in 2017 driven by strong inflows into capital markets.
In global commodity trade, Brent crude is trading at USD 66.87 a barrel.
Meanwhile, domestic equity markets got off to a poor start on the first session of the New Year -- suffering their biggest single-day loss in one month following heavy fag-end selling in auto, banking and IT.
Besides, a lack of fresh cues due to closure of global bourses in view New Year holiday also had impact on domestic equities.
Indian markets emerged as the third-best performer in Asian region, which rewarded investors by a handsome 29 per cent in 2017.
The benchmark Sensex retreated from its record high to end at 33,812.75 with a sharp cut of 244 points, while the Nifty tumbled over 95 points at 10,435.55.
At the Interbank Foreign Exchange (forex) market, the domestic unit opened a tad higher at 63.85 against the last weekend level of 63.87 and traded in a narrow range.
But, later breaking the momentum trading, it shot up to hit an intra-day high of 63.64 in mid-afternoon deals before winding up the strong session with a solid 19 paise gain at 63.68.
The RBI, meanwhile, fixed the reference rate for the dollar at 63.6697 and for the euro at 76.4100.
All major world markets are closed today for new year holiday.
The dollar fell to its lowest in over three months against a basket of major currencies on Friday, marking its steepest annual drop since 2003, on doubts over durability of a pickup in US economic growth in wake of last week's tax overhaul.
In cross-currency trades, the rupee rebounded sharply against the pound sterling to finish at 85.91 per pound from 86.27 and also bounced back against the euro to end at 76.40 compared to 76.53 earlier.
The local currency remained firm against the Japanese yen to conclude at 56.52 per 100 yens from 56.77 previously.
In forward market today, premium for dollar drifted owing to mild receiving from exporters.
The benchmark six-month premium payable in June moved down to 138-140 paise from 139-141 paise and the far forward December 2018 contract also slipped to 274.50-276.50 paise from 276-278 paise last Friday.
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