Forex traders said rising US-China tension weighed on the local currency even as positive domestic equities and improving risk appetite supported the local unit.
The rupee opened weak at 75.90 at the interbank forex market, down 19 paise over its last close.
It had settled at 75.71 against the US dollar on Wednesday.
"Asian currencies are weak this Thursday morning after US President Donald Trump said he was working on a strong response to China''s proposed security law in Hong Kong," Reliance Securities said in a research note.
It further said that currencies could track the local equities during the session amid optimism over the reopening of economies combined with monetary and fiscal support the respective economies.
On the domestic equity market front, the 30-share benchmark Sensex was quoting 321.01 points higher at 31,926.23 and the broader Nifty rose 84.40 points to 9,399.35.
Foreign institutional investors were net sellers in the capital market, as they sold equity shares worth Rs 334.74 crore on Wednesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 2.48 per cent to USD 33.88 per barrel.
The dollar index, which gauges the greenback''s strength against a basket of six currencies, fell by 0.08 per cent to 98.98.
Meanwhile, in India, the death toll due to COVID-19 rose to 4,531 and the number of cases climbed to over 1.58 lakh in the country, according to the Health Ministry.
The number of cases around the world linked to the disease has crossed over 56.93 lakh and the death toll has topped 3.55 lakh. PTI DRR ANS