However, strengthening of the greenback vis-a-vis other currencies overseas capped gains for the rupee, forex dealers said.
At the interbank foreign exchange, the rupee opened strong at 70.75, showing a gain of 15 paise over its previous closing.
On Friday, the rupee had appreciated by 12 paise to settle at 70.90 against the US dollar.
Forex market remained closed on Monday on account of ‘Diwali Balipratipada’.
A higher opening in the domestic equities supported the local unit.
The BSE Sensex was trading 106.37 points, or 0.27 per cent, higher at 39,356.57 in morning trade, and the broader NSE Nifty advanced 16.75 points, or 0.14 per cent, to 11,643.90.
Meanwhile, brent crude futures, the global oil benchmark, fell 0.18 per cent to USD 61.46 per barrel.
The dollar index, which gauges the greenback’s strength against a basket of six currencies, rose 0.02 per cent to 97.78.
In the special Muhurat trading session, foreign institutional investors remained net buyers in the capital markets, putting in Rs 6.61 crore on Sunday, according to provisional exchange data.
FIIs had sold shares worth Rs 435.42 crore on Friday, while domestic institutional investors bought to the tune of Rs 440.16 crore, as per the data.
The 10-year government bond yield was at 6.52 per cent in morning trade.