The overall forex market sentiment got a boost from upbeat export data and narrowing of trade deficit coupled with softening inflation.
The record rally in domestic equities too helped the rupee.
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It later strengthened to hit a fresh intra-day high of 64.69 before winding up the day at 64.74, showing a smart rise of 19 paise, or 0.29 per cent.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.7603 and for the euro at 76.3912.
India's economic recovery has been patchy of late, post demonetisation and the newly introduced GST regime, but the recent data seems to be suggesting increased optimism, a forex dealer commented.
The GDP expansion hit a three-year low of 5.7 per cent in the April-June quarter with India losing the fastest-growing economy tag to China for the second straight quarter.
The latest data revealed that India's export soared by 25.67 per cent to USD 28.61 billion in September on rise in shipments of chemicals, petroleum and engineering products.
Import too rose by 18.09 per cent to USD 37.6 billion in September from USD 31.83 billion in the year-ago month.
Trade balance stood almost flat at USD 8.98 billion in September 2017 against USD 9 billion in September 2016.
Bearish dollar overseas along with robust capital inflows also supported the rupee.
Overseas investors have pumped a staggering USD 1.5 billion into the country's debt markets in the first two weeks of this month, primarily due to "positive real interest rates" and lower currency volatility.
However, in view of higher stock valuations, foreign portfolio investors (FPIs) pulled out Rs 1,775 crore (USD 272 million) from equities during this period.
Meanwhile, domestic bourses displayed a spectacular pre-Diwali fireworks with both indices scaling historic peaks on growing optimism for an economic recovery on the back of extremely bullish macro data, also supported by encouraging Q2 earnings from Reliance Industries.
The Sensex shot up over 200 points to end at historic high of 32,633.64, while Nifty jumped 63 to close at a life- time high of 10,230.85.
On the global front, the greenback traded modestly higher against its major trading rivals after the Federal Reserve chair Yellen confirmed her commitment of gradual interest rate hikes on the back of strong and broad based US growth.
The dollar index, which measures the greenback's value against a basket of six major currencies, was trading higher at 93.05 in early trade.
In cross-currency trades, the rupee recovered against the pound sterling to finish at 86.10 from 86.30 per pound and hardened against the Euro to close at 76.48 from 76.74 earlier.
The local currency, however dropped against the Japanese yen to settle at 57.94 per 100 yens from 57.88 last Friday.
In forward market today, premium for dollar displayed a mixed trading owing to lack of market moving factors.
The benchmark six-month premium payable in March softened to 121-123 paise from 122-124 paise, while far forward September 2018 contract edged up to 260-262 paise from 259.50-261.50 paise.
On the international energy front, crude prices jumped on Monday.
International Brent crude futures rose 84 cents, or 1.5 per cent, to USD 58.01 per barrel in early Asian trade, after trading as high as USD 58.15.
US West Texas Intermediate crude was at USD 52.16 per barrel, up 71 cents or 1.4 percent.
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