The rupee depreciated by 4 paise to 82.67 against the US dollar in early trade on Tuesday, tracking a strong American currency against major rivals overseas.
Forex traders said downward movement in crude price and inflows of foreign funds, however, capped the fall in the Indian currency.
Meanwhile, the dollar strengthened as investors were upbeat on the tentative agreement between US President Joe Biden and Republican House Speaker Kevin McCarthy on the debt ceiling, which is likely to face voting on Wednesday before getting sealed.
Traders were also keeping an eye on the US non-farm payroll (NFP) data to be released on Friday.
"Rupee traded in a narrow range and volatility remained low as most market participants remained on the sidelines following US market holiday. On the othe hand, the dollar was weighed down after preliminary talks between the Republicans and Democrats sailed through.
"Today, focus will be on the consumer confidence number from the US and that is likely to trigger volatility for the dollar; more updates on the debt ceiling vote will also be important to watch. We expect the USDINR (Spot) to trade sideways and quote in the range of 82.40 and 82.80," said Gaurang Somaiya, FX and bullion analyst at Motilal Oswal.
At the interbank foreign exchange, the domestic unit opened flat at 82.63 against the dollar and hit the lowest level of 82.69. Later, it touched 82.67, registering a fall of 4 paise over its previous close.
On Monday, the rupee closed at 82.63 against the US currency.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.09 per cent to 104.30.
Brent crude futures, the global oil benchmark, fell 0.61 per cent to USD 76.60 per barrel.
In the domestic equity market, the 30-share BSE Sensex advanced 123.87 points or 0.20 per cent to 62,970.25. The broader NSE Nifty was up 35.50 points or 0.19 per cent to 18,634.15.
Foreign Institutional Investors (FIIs) were net buyers in the capital market on Monday as they purchased shares worth Rs 1,758.16 crore, according to exchange data.
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