This is the highest close for the rupee since June 9 when it had settled at 64.24 against the US dollar.
Smooth supply of dollars on the back of abundant capital inflows into equities and debts predominantly weighed on trading sentiment.
Besides, a spectacular rebound in domestic equities supported the rupee rise.
At the Interbank Foreign Exchange (forex) market, the rupee opened virtually steady at 64.33 in a cautious and lacklustre trade.
After trading in a narrow range with a negative bias most part of the day, it recouped losses towards the fag-end trade and managed to settle at the highest level of 64.28, showing a smart gain of 5 paise, or 0.06 per cent.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.3211 and the euro at 74.2265.
The local unit has appreciated by a good 17 paise in the last three days.
Domestic financial markets staged a splendid comeback after a massive overnight rout following frantic low-level buying in beaten down counters even as healthcare and FMCG stocks supported the recovery momentum on the back of better-than-expected corporate earnings so far.
In cross-currency trades, the rupee fell back against the pound sterling to end at 83.76 from 83.73 per pound but recovered against the euro to finish at 74.05 from 74.29 earlier.
It also rebounded against the Japanese yen to close at 57.37 per 100 yens from 57.38 yesterday.
On the global front, the dollar traded near its multi- month lows against a currency basket in the wake of a steep sell-off sparked by fears that US President Donald Trump is having difficulties implementing his policy agenda.
The euro pulled back from its highest level since May 2016 against the US dollar on Wednesday as traders attention turned to Thursday's ECB policy meet outcome.
In forward market today, premium for dollar continued to trade little changed owing to lack of market moving factors.
The benchmark six-month premium payable in December edged lower to 132.5-134.5 paise from 134-135 paise and the far forward June 2018 contract also softened to 281-283 paise from 282-283 paise.
On the international commodity front, crude prices rose on Wednesday, supported by strong demand for gasoline, but rising output from OPEC producers revived concerns about a persistent overhang of excess crude.
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