This is the rupee's highest closing since August 10, 2015, when it had ended at 63.87 against the US dollar.
The forex market sentiment remained broadly supported after retail inflation dropped sharply to 2.99 per cent in April from 3.90 per cent in March while wholesale inflation (as per new series) slipped to a four-month low of 3.85 per cent.
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The rupee opened extremely bullish at 64.12 as against last weekend level of 64.31 at the Interbank Foreign Exchange market amid smooth supply of the US currency.
It strengthened further to hit a fresh intra-day high of 64.03 before ending at 64.05, revealing a rise of 26 paise, or 0.40 per cent.
The local unit has appreciated by a healthy 58 paise in the last three sessions.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.1188 and for the euro at 70.1332.
Growing evidence of receding inflationary pressures fuelled further optimism over the strength of the economic recovery and added to expectations for the RBI to cut interest rates.
Besides, a smart rally in local equities along with massive capital inflows also aided the rupee spike.
According to latest depository data, FPIs invested a net Rs 5,318 crore ($825 million) in debt markets during May 2-12.
Domestic equities closed at a new record high on hardening expectations of a rate cut by the Reserve Bank of India after consumer inflation eased in April to its lowest in at least five years.
The flagship Sensex shot up 134 points to end at 30,322.12, while broader Nifty jumped by 44.50 points at 9,445.40.
Meanwhile, the greenback started the week on the defensive after US economic data came in shy of expectations and a weekend missile test by North Korea further fuelled the political turmoil globally.
Global crude oil soared after Saudi Arabia and Russia voice support for extending the Organisation of the Petroleum Exporting Countries (Opec)-led production cut scheme due to expire mid-year through the first quarter of 2018.
The dollar index, which tracks the US currency against a basket of six major rivals, was down 0.36 per cent at 98.69.
In cross-currency trades, the rupee fell back against the pound sterling to finish at 82.81 from 82.64 per pound and also retreated against the euro to close at 70.26 as compared to 69.96 earlier.
However, it regained some lost ground against the Japanese Yen to end at 56.45 per 100 yens from 56.48 earlier.
In forward market on Monday, premium for dollar showed a steady trend due to lack of market moving factors.
The benchmark six-month premium payable in October and the far forward April 2018 contract ended unchanged at 145-147 paise and 299-301 paise, respectively.
In the international commodity front, crude prices surged more than 2 per cent on Monday to trade at $52 a barrel after top exporter Saudi Arabia and Russia said supply cuts needed to last into 2018, a step towards keeping an Opec-led deal to support prices in place longer than originally agreed.
The Brent crude, the global benchmark, was trading up $1.20 at $52.04 a barrel in early Asian trade.
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