The rupee depreciated 3 paise to 83.13 against the US dollar in early trade on Tuesday amid firm crude oil prices and outflow of foreign funds from domestic equity markets.
The rupee, however, found support due to marginal weakness in American currency and positive sentiment in the equity markets, forex traders said.
At the interbank foreign exchange, the domestic currency opened at 83.10 against the dollar and then slipped to 83.13 gainst the greenback, registering a fall of 3 paise over its previous close. In early deals, the local unit was oscillating between 83.09 and 83.13 versus dollar.
On Monday, the Indian currency settled at 83.10 against the dollar.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.01 per cent lower at 102.17.
Global crude oil price benchmark Brent crude rose by 0.17 per cent to USD 78.08 per barrel.
In the domestic equity market, the 30-share BSE Sensex was trading 31.03 points or 0.04 per cent higher at 71,346.12. The broader NSE Nifty was up 15.60 points or 0.07 per cent to 21,434.25.
Foreign institutional investors (FIIs) were net sellers in the equity market on Monday despite hectic activity. FIIs bought shares worth Rs 11,473.54 crore and sold equities worth Rs 11,507.05 crore, leading to a net outflow Rs 33.51 crore, according to exchange data.