Among a range of factors responsible for positive sentiment, the recent pick-up in the macroeconomic indicators led from the front in driving the rally.
Overall forex market sentiment also got a positive vibe generally after US lawmakers reached a deal to end a Federal government shutdown.
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Striking an upbeat note, the International Monetary Fund (IMF) projected the Indian economy to grow at 7.4 per cent in 2018 -- making it the fastest growing major economy.
The Indian rupee charged southwards in the previous session, impacted by US political jitters.
Though currency traders remained little cautious ahead of the current NDA government's last full-year Union budget before the 2019 general elections and RBI's policy meet, a forex dealer said.
The home currency resumed slightly weak at 63.88 as compared to 63.87 previously at the Interbank Foreign Exchange (forex) market.
Succumbing to modest dollar pressure, it lost further ground to touch a low of 63.91 in mid-morning deals before staging a smart recovery.
After hitting day's high of 63.75 towards the tail-end session, the local unit finally settled at 63.78, showing a gain of 9 paise, or 0.14 per cent.
The RBI meanwhile fixed the reference rate for the dollar at 63.7722 and for the euro at 78.2166.
On the international commodity front, crude prices rose, lifted by healthy global economic growth projections by the IMF as well as the ongoing supply curtailments by a group of exporters, including Opec and Russia.
Brent crude futures were trading higher at $69.27 a barrel in early Asian trading.
In the meantime, the domestic bourse continued its longest record-winning streak in years with both the benchmark indices notching new milestones driven by investors' optimism in the face of robust earnings trends amid bullish global sentiment.
Asian stock also gained across the board even as US indices hit fresh record highs overnight.
The flagship BSE-Sensex shot up 342 points to close above 36,000-mark, while Nifty surged 118 points to a record 11,083.70.
On the global front, the greenback held onto modest gains against other major currencies, supported by news a deal to temporarily end the US government shutdown was made amid growing concern over the US stance on global trade.
The dollar index, which measures the greenback's value against a basket of six major currencies, was up at 90.29 in early trade.
In cross-currency trades, the rupee drifted further against the pound sterling to end at 88.95 per pound from 88.79 and continued to slide against the Japanese yen to close at 57.77 per 100 yens from 57.70 earlier.
The home unit moved up against the euro to finish at 78.10 from 78.25 yesterday.
Elsewhere, the euro hardened further against the US dollar after the latest survey results revealed an optimistic outlook for the German economy in the first six months of 2018 also supported by the ECB's monetary policy meeting this week.
The British pound, however, traded weak against the greenback after the IMF downgraded the UK growth outlook on Monday amid fading optimism over the Brexit negotiation.
The Japanese yen also moved in a narrow range against the US dollar after the Bank of Japan decided to leave the monetary policy unchanged, saying inflation is creeping towards the target.
In forward market today, premium for dollar weakened further owing to sustained receiving from exporters.
The benchmark six-month forward premium payable in June softened to 121-123 paise from 122-124 paise and the far- forward December 2018 contract also edged down to 257.50- 259.50 paise from 259-261 paise on Monday.
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