Mumbai, Jun 30 (PTI) The rupee on Tuesday appreciated by 7 paise to 75.51 against the US dollar on softening crude oil prices and early gains in domestic equity market.

Forex traders said the rupee traded in a narrow range as positive domestic equities supported the local unit, while foreign fund outflows and concerns over rising COVID-19 cases weighed on investor sentiment.

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The rupee opened strong at 75.48 and settled for the day at 75.51 against the US dollar, up 7 paise over its previous close.

It had settled at 75.58 against the greenback on Monday.

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During the four-hour trading session, the domestic unit saw an intra-day high of 75.45 and a low of 75.58 against the American currency.

Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.09 per cent to 97.62.

Brent crude futures, the global oil benchmark, fell 0.62 per cent to USD 41.45 per barrel.

Paring the early gains, key stock indices closed marginally lower as investors turned cautious ahead of Prime Minister Narendra Modi's address to the nation after market hours.

The 30-share index settled 45.72 points, or 0.13 per cent, down at 34,915.80 while the NSE Nifty slipped 10.30 points, or 0.10 per cent, to 10,302.10.

Foreign institutional investors were net sellers in the capital market as they sold shares worth Rs 1,937.06 crore on Monday, according to provisional exchange data.

In his address to the nation, the Prime Minister announced extension of the Pradhan Mantri Garib Kalyan Anna Yojana (PMGKAY), a free ration scheme, for 80 crore people across the country till end of November. He said it will cost the government Rs 90,000 crore more.

"Rupee strengthened in six out of last seven sessions following foreign fund inflows, central bank dollar selling, steady crude oil prices and lower dollar index," HDFC Securities Deputy Head of Retail Research Devarsh Vakil said, adding that positive data surprises in the US and China (PMIs) have supported risk sentiment.

Market participants were cautious ahead of Prime Minister Narendra Modi's address after the market hours, fiscal deficit and eight core infra number release.

Official data showed that the output of eight core infrastructure industries shrank by 23.4 per cent in May due to the coronavirus-induced lockdown.

"Rupee ended the quarter on strong note after plunging 5.95 per cent in the March quarter. The near term range for rupee remains between 75 to 76.50," Vakil said.

According to Jateen Trivedi, Senior Research Analyst (Commodity & Currency) at LKP Securities, "Rupee traded in range but with minor weakness as USDINR took support near 75.40 and bounced towards 75.60 on back of some buying witnessed due to uncertainty on risky assets and higher crude prices & Gold prices."

Meanwhile, the number of cases around the world linked to the COVID-19 has crossed 1.03 crore and the death toll has topped 5.05 lakh.

In India, the death toll due to COVID-19 rose to 16,893 and the number of infections spiked to 5,66,840, according to the health ministry.

The Financial Benchmark India Private Ltd (FBIL) set the reference rate for the rupee/dollar at 75.5680 and for rupee/euro at 85.1173. The reference rate for rupee/British pound was fixed at 93.5829 and for rupee/100 Japanese yen at 70.57.

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