The rupee appreciated 23 paise to 75.93 against the US dollar in the opening trade on Tuesday, following a positive trend in domestic equities amid softening global crude oil prices.
A weak American currency in the overseas market also helped the domestic unit, forex traders said.
At the interbank foreign exchange, the rupee opened strong at 75.97 against the US dollar and gained further ground to quote at 75.93, a rise of 23 paise over the previous close.
In the previous session, the rupee had settled at 76.16 against the greenback.
Global oil benchmark Brent crude futures declined 1.53 per cent to USD 110.76 per barrel.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, slipped 0.06 per cent to 98.99.
On the domestic equity market front, the 30-share Sensex was trading 233 points or 0.40 per cent higher at 57,826.49, while the broader NSE Nifty surged 75.85 points, or 0.44 per cent, to 17,297.85.
Foreign institutional investors remained net sellers in the capital market on Friday as they sold shares worth ₹80,1.41 crore, according to stock exchange data.
According to the latest public debt management report, the government's total liabilities rose to ₹128.41 lakh crore in the December quarter from ₹125.71 lakh crore in the three months ended September 2021.
The increase reflects a quarter-on-quarter increase of 2.15 per cent in October-December 2021-22.
The report released by the finance ministry on Monday said public debt accounted for 91.60 per cent of the total outstanding liabilities in the December quarter compared to 91.15 per cent at the end of September.