However, sustained foreign fund outflows and a weak trend in domestic equities restricted the appreciation bias to some extent.
At the interbank foreign exchange market, the local unit opened at 82.87 and touched an intra-day high of 82.74 and a low of 82.91 against the greenback.
It finally settled at 82.82, registering a rise of 18 paise over its previous close.
On Tuesday, the rupee had slumped 22 paise to close at its all-time low of 83 against the dollar.
"The Indian rupee snapped a two-day fall as the dollar index wiped out most gains of Tuesday and crude oil declined more than 2 per cent to USD 80 a barrel. The stronger Asian currencies and suspected RBI intervention around 83 also supported the local unit," said
The dollar index, which gauges the greenback's strength against a basket of six currencies, declined 0.52 per cent to 103.97.
On the domestic equity market front, the 30-share BSE Sensex declined 636.75 points or 1.04 per cent to end at 60,657.45, while the broader NSE Nifty fell 189.60 points or 1.04 per cent to 18,042.95.
Global oil benchmark Brent crude futures fell 2.13 per cent to USD 80.35 per barrel.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Tuesday as they offloaded shares worth Rs 628.07 crore, according to exchange data.
Meanwhile, the Indian services sector growth touched a six-month high in December, supported by a robust intake of new work and favourable market conditions, a monthly survey said on Wednesday.
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