The rupee depreciated 12 paise to 75.27 against the US dollar in opening trade on Thursday tracking weakness in Asian peers and strengthening American currency.
The rupee opened at 75.23 at the interbank forex market, then lost ground and touched 75.27 against US dollar, down 12 paise over its last close.
It had settled at 75.15 against the US dollar on Wednesday.
Forex traders said positive opening in domestic equities supported the rupee, while factors like strong dollar, foreign fund outflows and rising COVID-19 cases dragged the local unit down.
"Cues from Asia remained weak as currencies in the continent were weak against the US dollar this morning," Reliance Securities said in a research note.
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.04 per cent to 96.11.
On the domestic equity market front, the 30-share BSE benchmark Sensex was trading 282.22 points higher at 36,334.03 and broader NSE Nifty rose 60.20 points to 10,678.40.
Foreign institutional investors were net sellers in the capital market as they offloaded shares worth Rs 221.70 crore on Wednesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 0.62 per cent to USD 43.52 per barrel.
Meanwhile, the number of cases around the world linked to COVID-19 has crossed 1.35 crore and the death toll has topped 5.83 lakh.
In India, the death toll due the disease rose to 24,915 and the number of infections rose to 9,68,876, according to the health ministry.