The rupee witnessed range-bound trade and depreciated 2 paise to 84.07 against the US dollar in initial deals on Tuesday, weighed down by significant foreign fund outflows, elevated crude oil prices and the strength of the American currency in the overseas market.

Forex traders said the rupee is trading in a narrow range as the support from positive domestic equities is being negated by foreign fund outflows. Moreover, crude oil prices have also surged by 10 per cent, ballooning India's already worrisome trade deficit.

At the interbank foreign exchange, the rupee opened at 84.06 against the greenback and traded in a tight range. In the initial trade, it touched 84.07, registering a fall of 7 paise over its previous close.

On Monday, the rupee recovered from its all-time low levels and appreciated 5 paise to close at 84.05 against the US dollar.

Indian rupee was stable on Monday as the Reserve Bank of India (RBI) supported it near to 84.08 levels, however, consistent US dollar bids from FPIs and oil companies weighed on the local unit, said Anil Kumar Bhansali, Head of Treasury and Executive Director Finrex Treasury Advisors LLP.

"Rupee would open flat but the watch will remain on what the RBI does to protect it," Bhansali added.

Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.05 per cent lower at 103.25.

Brent crude, the global oil benchmark, declined 2.89 per cent to USD 75.22 per barrel.

On the domestic equity market front, Sensex advanced 222.53 points, or 0.27 per cent, to 82,195.58 points. The Nifty rose 57.85 points, or 0.23 per cent, to 25,185.80 points.

Foreign institutional investors (FIIs) were net sellers in the capital markets on Monday, as they offloaded shares worth Rs 3,731.59 crore, according to exchange data.

On the domestic macroeconomic front, soaring vegetable prices pushed the retail inflation rate to a nine-month high of 5.49 per cent in September, according to government data released on Monday.

The consumer price index (CPI)--based retail inflation was 3.65 per cent in August and 5.02 per cent in September 2023. The previous high inflation rate was witnessed in December 2023 at 5.69 per cent.

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