This is the best closing level for the Indian currency since August 9, when it had settled at 63.84.
The rupee today opened higher at 63.93 against last Thursday's close of 64.04 at the forex market.
The domestic currency hit a fresh intra-day high of 63.85 in late afternoon deals before ending at 63.91, registering a smart gain of 13 paise, or 0.20 per cent.
Overall forex market sentiment also got a boost from easing of border tensions between India and China following a diplomatic breakthrough on months-long stand-off.
India and China have agreed to "expeditious disengagement" of border personnel at Doklam, New Delhi said today, a week before the BRICS summit in China that Prime Minister Narendra Modi is expected to attend.
A strong showing by local equities along with extreme bearish dollar overseas mood also largely supported the rupee upsurge, a forex dealer commented.
The greenback continued its prolonged Fed-driven weakness against all its major rivals on growing concerns about US President Donald Trump's ability to drive his economic agenda even as the heavily anticipated speech by Federal Reserve Chair Janet Yellen in Jackson Hole failed to provide stronger policy guidance.
The flagship Sensex shot up by over 154 points to end at 31,750.82, while NSE Nifty recaptured the 9,900-mark by surging about 56 points to close at 9,912.80.
The dollar index, which measures the greenback's value against a basket of six major currencies, was sharply down at 92.41.
In cross-currency trades, the rupee fell back against the pound sterling to finish at 82.53 from 82.07 per pound and also drifted sharply against the euro to settle at 76.22 from 75.54 earlier.
The euro extended gains to a two-and-a-half year high against the dollar on Monday after the European Central Bank president held back from talking down the currency and also concerns about the impact of Tropical Storm Harvey on the US economy.
In forward market today, premium for dollar remained weak due to consistent receivings from exporters.
The benchmark six-month premium payable in January eased to 118-120 paise from 120.50-122.50 paise and the far forward July 2018 contract also moved down to 255-257 paise from 257- 259 paise.
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