The rupee depreciated 10 paise to 83.50 against the US dollar in early trade on Monday, largely due to the rise in the dollar index and US yields.

Forex traders said uncertainty among market players was down as Narendra Modi was sworn in as Prime Minister on Sunday for a record-equalling third term. However, the strength of the American currency in the international market weighed on the local unit.

At the interbank foreign exchange market, the local unit opened at 83.48 and lost further ground to trade at 83.50 against the greenback, registering a loss of 10 paise from its previous closing level.

On Friday, the rupee appreciated 13 paise to 83.40 against the US dollar.

According to Anil Kumar Bhansali, Head of Treasury and Executive Director Finrex Treasury Advisors LLP, the rupee opened at 83.50 largely due to the rise in the dollar index and US yields.

"The Reserve Bank of India (RBI) should be present protecting the rupee as existing policies of the government will continue with largely the same cabinet as in Modi-2.0," Bhansali said.

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.

Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading at 105.18, higher by 0.29 per cent.

Brent crude futures, the global oil benchmark, advanced 0.31 per cent to $79.87 per barrel.

On the domestic equity market, both benchmark indices, Sensex and Nifty, scaled record high levels in initial trade. The 30-share BSE Sensex was trading 292.08 points, or 0.38 per cent higher at 76,985.44 points. The broader NSE Nifty was trading at 23,291.50 points.

Foreign Institutional Investors (FIIs) were net buyers in the capital markets on Friday, as they purchased shares worth ₹4,391.02 crore, according to exchange data.

Meanwhile, India's forex reserves jumped $4.837 billion to a new all-time high of $651.51 billion for the week ended May 31, the RBI said on Friday.

In the previous reporting week, the overall reserves had dropped $2.027 billion to $646.673 billion.