At the interbank foreign exchange, the local unit opened at 83.48 and settled for the day lower by 10 paise at 83.50 (provisional) against the American currency.
On Friday, the rupee appreciated 13 paise to 83.40 against the US dollar.
"We expect the rupee to trade with a slight negative bias on strong US Dollar amid rising expectations of a delay in interest rate cut by the US Federal Reserve due to tight job market," said Anuj Choudhary - Research Analyst at Sharekhan by BNP Paribas.
However, softening crude oil prices and optimism over a stable government may support the rupee at lower levels. Traders may take cues from inflation data from India and the US.
Investors may also watch out for the Federal Open Market Committee (FOMC) meeting this week. USD/INR spot price is expected to trade in a range of INR 83.20 to INR 83.80.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading at 105.27, higher by 0.37%.
Brent crude futures, the global oil benchmark, advanced 0.21% to USD 79.79 per barrel.
Modi will be heading a 72-member Union Council of Ministers putting emphasis on continuity, youth and experience, while also rewarding partners in the BJP-led National Democratic Alliance (NDA) government.
Along with Modi, senior BJP leaders including Rajnath Singh, Amit Shah, Nitin Gadkari, Nirmala Sitharaman and S Jaishankar, all ministers in the Modi 2.0 cabinet, took oath as cabinet ministers at the Rashtrapati Bhavan.
On the domestic equity market, the 30-share BSE Sensex declined 203.28 points, or 0.27%, to close at 76,490.08 points. The broader NSE Nifty settled 30.95 points or 0.13% lower at 23,259.20 points.
Foreign Institutional Investors (FIIs) were net buyers in the capital markets on Friday, as they purchased shares worth INR 4,391.02 crore, according to exchange data.
Meanwhile, India's forex reserves jumped USD 4.837 billion to a new all-time high of USD 651.51 billion for the week ended May 31, the RBI said on Friday.
In the previous reporting week, the overall reserves had dropped USD 2.027 billion to USD 646.673 billion.
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