Weak dollar sentiment overseas largely supported the recovery movement even as heightened geopolitical worries continue to dominate at the global level.
A smart relief rally in local equities also kept forex market tone buoyant.
The rupee had tumbled by a whopping 28 paise yesterday.
Brushing aside global volatility, domestic bourses witnessed a splendid rally, breaking a three-day string of declines on the back of value buying in key blue-chip stocks. Most Asian stocks ended lower.
The greenback fell back in Asian trading, as concerns over tensions with North Korea and Syria largely weighed on US Treasury yields amid fading Fed rate hike fears.
Federal Reserve Chair Janet Yellen struck her usual cautiously upbeat note on the US economy in a speech on Monday, but failed to move the dial for markets either way.
At the Interbank Foreign Exchange market (forex), the home currency resumed substantially lower at 64.65 against Monday's close of 64.56 on fresh bouts of dollar demand from importers and drifted further to 64.69.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.5438 and for the euro at 68.3067.
The dollar index, which tracks the US currency against a basket of six major rivals, was trading lower on the day at 100.73.
In cross-currency trade, the rupee moved down further against the pound sterling to finish at 80.15 from 80.04 per pound and fell back sharply against the euro to close at 68.43 compared to 68.24 earlier.
On the equity front, the flagship Sensex rebounded over 212 points to close at 29,788.35, while broader Nifty rose 55.55 points at 9,237.
In the forward market today, premium for dollar displayed a lacklustre trend owing to lack of market moving factors.
The benchmark six-month premium for September advanced to 156-157 paise from 155.5-156.5 paise, while the far-forward March 2018 contract was quoted at 312-314 paise from 313-314 paise on Monday.
In the global commodity front, crude prices eased a little through the Asia-Pacific session but mostly holding its five-week highs amid growing geopolitical worries.
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