The domestic currency market largely withstood the global bonds meltdown as well as the sell-off in local bourses.
The Indian unit touched a fresh one-week low of 63.79 in early trade before recovering lost ground.
It traded in a tight range between 63.79 and 63.59 with negative bias most part of the session.
Sustained month-end demand from banks and importers predominantly weighed on the domestic unit even as traders await cues from the US Fed policy meet outcome.
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Meanwhile, domestic markets took a broad knock and retreated sharply from their record highs amid caution ahead of the Union Budget this week.
Most Asian bourses ended deep in the red reacting to a sharp fall on Wall Street.
The benchmark BSE Sensex tumbled 250 points to end at 36,033.73, while the Nifty slumped almost 81 points to 11,049.65.
On the global energy front, crude remained under pressure for the second day as a strengthening dollar along with rising US output pushed the price below USD 69 a barrel for the first time in six days.
Extending the bearish momentum, it touched a fresh intra-day low of 63.79 in mid-afternoon deals before staging a solid rebound to cut short early losses.
It settled the day with a modest 2 paise loss at 63.60 against the greenback.
The RBI, meanwhile fixed the reference rate for the dollar at 63.7534 and for the euro at 78.7546.
Globally, the US dollar erased early gains against other major currencies as investors were cautious ahead of President Donald Trump's State of the Union address and the Federal Reserve's monthly policy decision on Wednesday.
In cross-currency trades, the rupee fell back after a brief recovery against the pound sterling to end at 89.80 per pound from 89.43 and also drifted back against the euro to finish at 79.02 from 78.81 earlier.
It continued the fall against the Japanese yen to close at 58.59 per yens from 58.47 yesterday.
In forward market today, premium for the dollar showed lacklustre trading owing to lack of market moving factors.
The benchmark six-month forward premium payable in June inched up to 118-120 paise from 118.50-119.50 paise, while the far-forward December 2018 contract softened to 255.50-257.50 paise from 256.50-257.50 paise previously.