This is again the highest closing for the domestic currency since June 14, when it had hit 64.30.
A massive sell-off in local equities largely kept forex market sentiment little shaky despite the sluggish dollar tone overseas even as emerging market currencies remained subdued. The rupee opened marginally higher at 64.32 against Monday's closing of 64.35 in yet another day of extremely thin and lethargic trade at the Interbank Foreign Exchange (forex) market.
The local unit finally managed to settle higher at 64.33, revealing a small gain of 2 paise, or 0.03 per cent.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.3301 and for the euro at 74.1469.
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Robust FII inflows into equities and debt predominantly helped the home currency to stay afloat, a forex dealer commented.
Foreign portfolio investors (FPIs) bought shares worth a net Rs 328.61 crore yesterday, as per provisional data released by the stock exchanges.
In worldwide trade, the greenback traded substantially weak, hitting multi-month lows against its rivals after the Trump healthcare bill failed to get enough backing to proceed to a debate.
In cross-currency trades, the rupee recovered against the pound sterling to finish at 83.73 from 84.05 per pound, but remained weak against the euro to end at 74.29 from 73.76 yesterday.
It also declined further against the Japanese yen to close at 57.38 per 100 yens from 57.22 earlier.
The dollar index, which measures the greenback against a basket of currencies was sharply down at 94.50 - its lowest level in 10 months during Asia trade.
In forward market today, premium for dollar remained soft due to good receivings from exporters.
The benchmark six-month premium payable in December eased to 134-135 paise from 134.50-136.50 paise and the far forward June 2018 contract also edged lower to 282-283 paise as compared to 282-284 paise.
Brent crude futures were at USD 48.55 per barrel in early Asian trade.