The rupee strengthened by 13 paise to 79.11 against the US dollar in opening trade on Monday.
Forex traders said the rupee opened stronger as the dollar continued to fall on account of a less aggressive US Fed and falling crude oil prices.
At the interbank foreign exchange, the rupee opened at 79.16 against the US dollar and touched 79.11 in initial deals, registering a rise of 13 paise over the last close.
In the previous session, the rupee had closed at 79.24 against the US dollar.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.14 per cent to 105.75.
Global oil benchmark Brent crude futures fell 0.97 per cent to USD 103 per barrel.
According to Anil Kumar Bhansali, Head of Treasury, Finrex Treasury Advisors, the rupee is likely to trade in the range of 79 to 79.40.
"The market awaits the RBI MPC to give its rate signals on August 5," Bhansali said.
On the domestic equity market front, the 30-share Sensex was trading 188.86 points or 0.33 per cent higher at 57,759.11, while the broader NSE Nifty rose 72.45 points or 0.42 per cent to 17,230.70.
Foreign institutional investors were net buyers in the capital market on Friday, purchasing shares worth Rs 1,046.32 crore, as per exchange data.