Forex traders said a positive start of domestic stocks supported the local unit. Moreover, investor risk appetite is improving as India could relax restrictions in many areas from May 4.
At the interbank foreign exchange, the rupee opened at 75.17, then gained ground and touched 75.03, registering a rise of 63 paise over its previous close.
On Wednesday, rupee had settled at 75.66 against the US dollar.
Besides, market sentiments improved as more countries are announcing gradual lifting of lockdowns that have been imposed to contain coronavirus infection, traders said.
"Additionally, risk sentiments improved after an antiviral drug showed promise in treating coronavirus patients," Reliance Securities said in a research note.
Meanwhile, the dollar index, which gauges the greenback's strength against the basket of six currencies, was trading 0.02 per cent up at 99.58.
"US Dollar continued to remain under pressure this morning after the US Fed pledged to do more to support the economy battered by the business shutdowns due to the ongoing pandemic," Reliance Securities said.
Meanwhile, in India, the death toll due to COVID-19 rose to 1,074 and the number of cases climbed to 33,050 on Thursday, according to the Union Health Ministry.
The number of cases around the world linked to the disease has crossed over 31.93 lakh and the death toll has topped 2.27 lakh.
Domestic bourses were trading on a positive note on Thursday with benchmark indices Sensex trading 988.25 points higher at 33,708.41 and Nifty up 283 points at 9,836.35.
Foreign institutional investors were net buyers in the capital market, as they bought equity shares worth Rs 722.08 crore on Wednesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 9.54 per cent to USD 24.69 per barrel. DRR DRR ANSANS