At the interbank foreign exchange market, the local unit opened at 83.92 and then touched an early high of 83.84, registering a 25 paise gain from its all-time closing low of 84.09 against the American currency.
On Monday, the rupee slumped 37 paise to settle at an all-time low of 84.09 against the US dollar.
"The rupee is being sold off in good times and bad times indicating the demand for US dollar as foreign portfolio investors exit the Indian equity market on high valuation concerns," said Anil Kumar Bhansali Head of Treasury and Executive Director Finrex Treasury Advisors LLP
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, gained 0.16 per cent to 102.85 points.
Brent crude, the global oil benchmark, was trading at USD 77.15 per barrel in futures trade, on fears of spreading Middle East conflict that could hit supplies outweighing fears of a possible US recession that could hurt demand in the world's biggest oil consumer.
Moreover, Israel and US are bracing for a significant escalation after Iran and Hamas pledged to retaliate against Israel for killings last week of a Hamas Leader, traders said.
In the domestic equity market, the 30-share BSE Sensex rebounded 903.63 points, or 1.15 per cent, to 79,663.03 points, while the Nifty increased by 270.50 points, or 1.12 per cent, to 24,326.10 points.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Monday, as they offloaded shares worth Rs 10,073.75 crore, according to exchange data.