The rupee depreciated 6 paise to 75.60 against the US dollar in opening trade on Tuesday as strengthening American currency and sustained rise in crude oil prices weighed on investor sentiment even as domestic equities opened on a positive note.
Forex traders said, while firm start of the equity market and foreign fund inflows supported the rupee, factors like strong dollar, US-China tensions and Moody's downgrade of India's sovereign credit rating dragged down the local unit.
The rupee opened weak at 75.57 at the interbank forex market and then fell further to 75.60, down 6 paise over its last close.
It had settled at 75.54 against the US dollar on Monday.
"Risk appetite soured this morning as US President Donald Trump vowed to use force to end violent protests in American cities," Reliance Securities said in a research note, adding that Moody's downgrade and further downgrade expectation from other rating agencies could keep appreciation limited.
Moody's Investors Service on Monday downgraded India's sovereign credit rating for the first time in more than two decades.
Downgrading India's rating by a notch to 'Baa3' from 'Baa2' assigned in November 2018, Moody's estimated India GDP shrinking by 4 per cent -- first full fiscal contraction in more than four decades, as the country faces a prolonged period of slower growth.
Meanwhile, US President Donald Trump has threatened that he would deploy the military if the states fail to take necessary actions to quell the violent protests that have spread across the country over the custodial killing of African-American George Floyd.
Investors are also concerned about rising coronavirus cases and its impact on the global as well as domestic economy.
In India, the death toll due to COVID-19 rose to 5,598 and the number of the number of infections rose to 1,98,706, according to the health ministry.
The number of cases around the world linked to the disease has crossed 62.66 lakh and the death toll has topped 3.75 lakh.
On the equities front, the 30-share BSE benchmark Sensex was quoting 116.45 points higher at 33,419.97 and broader Nifty rose 35.55 points to 9,861.70.
Foreign institutional investors were net buyers in the capital market, as they bought equity shares worth Rs 1,575.46 crore on Monday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 0.94 per cent to USD 38.68 per barrel.
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose by 0.03 per cent to 97.86.
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