In early trade on Tuesday, the rupee fell 12 paise to 82.35 against the US dollar, owing to a stronger currency and foreign fund outflows from the domestic equity market.
At the interbank foreign exchange, the local unit opened lower at 82.27 versus the dollar then rose to 82.24 before slipping to 82.35.
The rupee closed at 82.23 versus the US dollar on Monday.
The dollar index, which measures the strength of the US currency against a basket of six currencies, increased 0.26 percent to 103.86.
Brent crude futures slid 1.08 percent to USD 79.90 per barrel, the global oil benchmark.
The 30-share BSE Sensex was trading 36.50 points, or 0.06 percent, higher at 58,274.35 points, while the wider NSE Nifty was up 38.85 points, or 0.23 percent, at 17,193.15 points.
According to exchange data, foreign institutional investors (FIIs) were net sellers in the capital markets on Monday, offloading shares worth Rs 1,546.86 crore.
The failure of two banks in the United States, Silicon Valley Bank and Signature Bank, has prompted concerns about the financial system's health, even as American regulators take steps to handle the issue.
In light of this, some analysts believe the US Federal Reserve may opt for a slower rate hike even if inflation remains high.
Domestically, retail inflation declined modestly in February to 6.44 percent, but remained above the Reserve Bank of India's tolerance zone of 6% for the second month in a row.
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