The rupee depreciated 9 paise to 79.03 against the US dollar in opening trade on Monday, as persistent foreign funds outflows weighed on investor sentiments.
Forex traders said the weakness of crude oil prices is supporting the local unit.
However, inflation and growth worries in India and globally could cap the appreciation bias, they added.
At the interbank foreign exchange, the rupee opened at 78.97 against the US dollar, then fell to quote 79.03, registering a decline of 9 paise over the last close.
In the previous session on Friday, the rupee had closed at 78.94 against the US dollar.
"Today is a US holiday therefore cash demand of USD will be absent. Maybe we could see some lower levels towards 78.80 for the pair. Importers should take advantage of the dips and buy their next 10-15 days of exposures and exporters could sell the upticks towards 79.20 for near-term exposures," said Anil Kumar Bhansali, Head of Treasury, Finrex Treasury Advisors.
On the domestic equity market front, the 30-share Sensex was trading 20.63 points or 0.04 per cent lower at 52,887.30, while the broader NSE Nifty fell 22.65 points or 0.14 per cent to 15,729.40.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was at 105.14.
Global oil benchmark Brent crude futures fell 0.08 per cent to $111.54 per barrel.
Foreign institutional investors remained net sellers in the capital market on Friday as they offloaded shares worth Rs 2,324.74 crore, as per exchange data.
Meanwhile, the country's foreign exchange reserves increased by $2.734 billion to $593.323 billion for the week ended June 24 on the back of a surge in the core currency assets, the Reserve Bank of India (RBI) said on Friday.