However, sustained foreign fund outflows and a weak trend in domestic equities dented investor sentiments.
At the interbank foreign exchange market, the local unit opened at 82.75 and touched an intra-day high of 82.50 and a low of 82.80 against the greenback.
It finally ended at 82.50 (provisional), registering a rise of 32 paise over its previous close.
On Wednesday, the rupee recovered from its all-time low level and settled at 82.82 against the dollar.
The dollar index, which gauges the greenback's strength against a basket of six currencies, declined 0.06 per cent to 104.18.
"The Indian rupee gained for a second day in trot supported by a weaker greenback and stronger regional peers. However, the gain was curtailed amid foreign fund outflows...," said
The December Federal Open Market Committee (
On the domestic equity market front, the 30-share
Global oil benchmark Brent crude futures rose 2.62 per cent to USD 79.88 per barrel.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Wednesday as they offloaded shares worth Rs 2,620.89 crore, according to exchange data.
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