The rupee depreciated 6 paise to 83.13 against the US dollar in the morning session, amid elevated crude oil prices and dollar demand from importers.
Forex traders said the rupee is trading in a narrow range as the support from positive domestic equities was negated by foreign fund outflows.
At the interbank foreign exchange, the rupee opened at 83.11 against the dollar, then fell to 83.13, registering a fall of 6 paise from its previous close.
In the initial trade, the rupee also touched an early high of 83.09 against the US dollar.
On Friday, the rupee settled at 83.07 against the US dollar.
Meanwhile, Brent crude futures, the global oil benchmark, was trading lower by 0.03 per cent to USD 80.04 per barrel.
"Brent oil crossed USD 80 per barrel after strong gains on supply concerns due to disruptions in the US and Russia triggered strong gains while caution before central bank meetings also kept prices muted," said Anil Kumar Bhansali, Head of Treasury and Executive Director Finrex Treasury Advisors LLP.
Bhansali further added that the inflows should dominate the session as RBI and oil companies buy dollars to protect any bigger gain on the rupee.
The dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.10 per cent lower at 103.22.
In the domestic equity market, the 30-share BSE Sensex was trading 475.55 points or 0.67 per cent higher at 71,899.20 points. The broader NSE Nifty rose 137.20 points or 0.64 per cent to 21,709.00 points.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Saturday as they offloaded shares worth Rs 545.58 crore, according to exchange data.
Meanwhile, India's forex reserves jumped USD 1.634 billion to USD 618.937 billion for the week ended January 12, the Reserve Bank of India (RBI) said on Friday.
In the previous reporting week, the overall reserves had declined sharply by USD 5.89 billion to USD 617.3 billion.