Despite a strong start, sustained demand for the American currency from banks and importers mainly hit the rupee movement at the forex market.
Speculative traders also reloaded their long-dollar positions tracking pessimistic global set-up.
However, robust capital inflows into equities and a recovery in domestic equities restricted the fall.
The home currency breached the key psychological 64-mark to hit a high of 63.9350 briefly in early trade before retreating.
At the Interbank Foreign Exchange market, the rupee resumed higher at 64.02 from last Friday's closing of 64.13 on fresh bouts of dollar selling by exporters.
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It then went on to hit an intra-day low of 64.14, but the local unit managed to recoup all losses to end flat at 64.12, showing a mere 1 paisa gain.
Domestic bourses saw a rebound after a five-session uninterrupted sell-off on the back of hectic short-covering as well as low level buying support with marked improvement in global sentiment following easing tensions between the US and North Korea.
Indian benchmark equity indices closed with a massive 3.5 per cent fall last week - its worst performance in one- and-a-half years.
Forex market will remain closed tomorrow in observance of Independence Day.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.0253 and for the euro at 75.7035.
The dollar index, which measures the greenback's value against a basket of six major currencies, was up at 93.21.
In cross-currency trades, the rupee strengthened further against the pound sterling to settle at 83.16 from 83.25 per pound and also bounced back against the Japanese yen to finish at 58.47 per 100 yens from 58.78.
In worldwide trade, the dollar traded higher against a basket of the other major currencies on Monday as some of the market volatility of last week eased and data showed that Japan's second quarter growth beat forecasts.
In forward market today, premium for dollar remained weak owing to persistent receivings from exporters.
The benchmark six-month premium payable in January moved down to 126-128 paise from 129-131 paise and the far-forward July 2018 contract also drifted to 259-261 paise from 263.50- 265.50 paise.
On the International commodity front, crude prices traded relatively soft as sentiment remained weak after sharper- than-expected slowdown in Chinese refining raised concerns about demand in the world's second-biggest consumer amid concerns over global supply glut.
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