The domestic currency managed to tide over the weak sentiment created by trade deficit ballooning to two-year high in November.
Overall forex market sentiment improved somewhat a day after the Federal Reserve's historic episode of monetary tightening, triggering panic dollar demand.
The home currency remained under pressure yesterday, tumbling by a whopping 40 paise in the midst of Fed-inspired volatility.
The US central bank raised rates by 25 bps to 50-75 bps on Wednesday for the first time in a year and projected its commitment of three rate hikes in 2017.
Growing confidence in country's growth outlook, which stands the best among its world peers at 7.3 per cent also bolstered the sentiment, he added.
At the Interbank Foreign Exchange (forex) market, the domestic unit opened steady at 67.83 but quickly fell back to a low of 67.86 on initial dollar demand.
However, overcoming the volatility, the rupee recouped smartly in afternoon deals to hit an intra-day high of 67.7325 before ending at 67.76, showing a gain of 7 paise or 0.10 per cent.
The US dollar index was quoted lower at 102.82 in late afternoon trade.
Meanwhile, the RBI today fixed the reference rate for the dollar at 67.7777 and euro at 70.7531.
In cross-currency trades, the rupee hardened further against the pound sterling to settle at 84.31 from 84.68 but retreated modestly against the euro to close at 70.78 from 70.66 yesterday.
shares worth a net Rs 225.84 crore yesterday, as per provisional data released by the stock exchanges.
Meanwhile, the benchmark Sensex rebounded by 145.71 points, or 0.52 per cent, to close at 28,301.27 today.
In forward market today, premium for dollar dropped on good receivings from exporters.
The benchmark six-month premium payable in July fell to 143-145 from its previous level of 148-150 and far forward January 2018 contract also declined to 294-296 from Wednesday's closing level of 299-301.
The RBI fixed the reference rate for the dollar at 66.9468 and for the euro at 71.0239.
The domestic currency dipped against the Japanese Yen to 58.96/98 per yen from 58.39/41 yesterday.
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