Later, the domestic unit was trading at 82.75 against the greenback, registering a fall of 10 paise.
On Wednesday, the rupee settled at 82.65 against the US dollar.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was 0.10 per cent lower at 104.54.
Global oil benchmark Brent crude futures rose 0.61 per cent to USD 74.14 per barrel.
The 30-share BSE Sensex was trading 116.67 points or 0.20 per cent lower at 57,439.23 points while the broader NSE Nifty was down 34 points or 0.2 per cent at 16,938.15 points.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Wednesday as they offloaded shares worth Rs 1,271.25 crore, according to exchange data.
Analysts said the failure of two banks in the US and crisis at Swiss banking major Credit Suisse have adversely impacted market sentiments.
On the domestic front, India's exports contracted in February for the third consecutive month, falling 8.8 per cent to USD 33.88 billion against USD 37.15 billion in the same month last year.
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