This is the highest closing for the domestic currency since June 14, when it ended at 64.30.
Bearish continuation in the greenback along with heavy unwinding of long dollar positions built up by speculative traders last week ahead of FOMC meet predominantly gave the rupee a boost.
Robust foreign fund inflows and a sustained record rally in domestic equities too backed up the rupee momentum.
The domestic unit opened firmly higher at 64.34 as compared to last weekend level of 64.45 at the Interbank Foreign Exchange (forex) market.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.3666 and for the euro at 73.6933.
In cross-currency trades, the rupee remained under immense pressure against the pound sterling and ended at 84.05 from 83.62 per pound and dropped further against the euro to finish at 73.76 from 73.57 earlier.
The local unit also fell back against the Japanese yen to settle at 57.22 per 100 yens from 56.96.
Bourses continued their relentless record breaking run on optimism about stellar corporate earnings even as beaten down technology heavyweights rallied handsomely amid highly bullish Asian cues.
Asian shares set a fresh two-year high, boosted by stronger-than-expected economic growth in China.
In the meantime, US dollar tumbled swift and hard under the impact of disappointing macro-economic data, raising doubts over the likelihood of a second rate hike from the Federal Reserve this year.
The greenback also touched multi-month lows against the euro, the British pound and the Australian dollar.
The dollar index, which measures the greenback against a basket of currencies slipped to trade as low as 94.93 during Asia trade on Monday, marking the lowest levels since September - before the US presidential election.
Meanwhile, China's economy expanded at an annual rate of 6.9 per cent in the second quarter an uptick on last year's 6.7 per cent expansion.
The benchmark six-month premium payable in December moved down to 134.50-136.50 paise from 136-138 paise and the far forward June 2018 contract edged down to 282-284 paise against 284-286 paise last Friday.
On the International commodity front, crude prices rebounded sharply for a combination of reasons including the massive drawdowns last week on both official crude inventory numbers and slowing oil production from the US amid buoyant expectations of strong refinery demand from China.
Brent crude futures were at USD 49.10 per barrel in early Asian trade.
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