The dollar index, which gauges the greenback's strength against a basket of six currencies, was down 0.65 per cent to 102.08, helping the rupee trade higher.
The domestic unit had closed at 75.12 against the US currency on Thursday.
Meanwhile, Indian stock indices slipped into the red after starting in positive terrain, with the BSE Sensex trading 23.79 points or 0.08 per cent lower at 28,264.44; and the NSE Nifty was down 19.75 points or 0.24 per cent at 8,243.70 in morning deals.
Investors continued to assess the impact of Covid-19 on the economy, impacting the trading sentiment on bourses.
According to the Health Ministry, the novel coronavirus cases in India rose to 195 on Friday after 22 fresh cases were reported from various parts of the country.
Foreign investors remained net sellers in Indian capital markets as they pulled out more than Rs 4,622.93 crore on Thursday, market data showed.
Brent crude futures, the global oil benchmark, rose 2.25 per cent to USD 29.11 per barrel.
The 10-year government bond yield was at 6.37 per cent in morning trade. DRR MKJ