However, weak trend in local equities and a firm US dollar overseas capped the rupee rise, a forex dealer said.
At the Interbank Foreign Exchange (Forex) market, the domestic currency resumed lower at 59.92 a dollar from last close of 59.78. It eased further to 59.93 due to initial dollar demand from importers and drop in local equities.
Later, it bounced back to a high of 59.67 on dollar selling by exporters and some banks before settling at 59.75, a rise of three paise or 0.05 per cent.
Yesterday, it had gained 23 paise or 0.38 per cent.
After plunging by 517.97 points or 1.98 per cent yesterday, the Indian benchmark S&P BSE Sensex today dropped further by 137.30 points or 0.54 per cent on concerns highlighted by the Economic Survey and reducing expectations from the Union Budget tomorrow.
FIIs had bought shares worth Rs 422.72 crore yesterday.
The dollar index, a gauge of six major global rivals, was up 0.04 per cent.
Pramit Brahmbhatt, Veracity Group CEO said: "Rupee ended slightly better for the day. Rupee appreciated as dollar selling from foreign banks helped it recover its early losses but weak local equities which closed half a per cent down weighed. The trading range for the spot USD/INR pair is expected to be within 59.30 to 60.30."
Meanwhile, the premium for forward dollar continued its downslide on consistent receipts by exporters.
The benchmark six-month premium payable in December dipped to 242-244 paise from 247-249 paise previously.
Far-forward contracts maturing in June, 2015 also dropped to 484.5-486.5 paise from 494-496 paise.
The Reserve Bank of India fixed the reference rate for dollar at 59.7260 and for the euro at 81.3800.
The rupee improved further against the pound to 102.23 from overnight close of 102.37 and also inched up to 81.26 per euro from 81.28.
It, however, closed a tad lower at 58.78 per 100 Japanese yen from 58.77.