Forex traders said buying in domestic equity market and weak American dollar supported the local unit.
The rupee opened on a strong note at the interbank forex market at 75.51 against the US dollar, up 14 paise over its last close.
It had settled at 75.65 against the US dollar on Thursday.
"The rupee is back in the familiar trading range of 75.40-75.95 that prevailed for a long time just prior to the spike above 76 on India-China border tensions. Intra-day USDINR is likely to trade 75.35-75.70 range with a down side bias," said Abhishek Goenka, Founder and CEO, IFA Global.
Goenka further added that "today (Friday) is the exchange traded currency derivative expiry for June. Month-end exporter-selling would likely cap upside. Asian currencies are stronger against the USD."
Forex traders said rising number of COVID-19 cases and its impact on global as well as domestic economy is weighing on investor sentiment.
The number of cases around the world linked to the disease has crossed 96.09 lakh and the death toll has topped 4.88 lakh.
Meanwhile, in India, the death toll due to COVID-19 rose to 15,301 and the number of the number of infections rose to 4,90,401, according to the health ministry.
On the equities front, the 30-share BSE benchmark Sensex was quoting 325.95 points higher at 35,168.05 and broader Nifty rose 102.85 points to 10,391.75.
Foreign institutional investors were net sellers in the capital market, as they sold equity shares worth Rs 1,050.61 crore on Thursday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 1.46 per cent to USD 41.65 per barrel.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell by 0.10 per cent to 97.32. DRR ANS ANS