The rupee depreciated 9 paise to 74.45 against the US dollar in opening trade on Thursday, tracking muted domestic equities.
The local unit opened at 74.44 against the greenback at the interbank forex market, then lost further ground and touched 74.45, down 9 paise over its last close.
On Wednesday, the rupee declined by 18 paise to close at 74.36 against the US dollar.
"The euphoria around a Joe Biden victory (in the US presidential election) and a vaccine becoming available by the year-end seems to be slowly settling down, said Abhishek Goenka, Founder and CEO, IFA Global.
The overall risk sentiment, however, continues to remain positive, he said, adding that the dollar though has made a comeback against majors and commodity currencies.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.02 per cent to 93.02.
On the domestic equity market front, the 30-share BSE benchmark Sensex was trading 202.76 points lower at 43,390.91, and the broader NSE Nifty fell 52.10 points to 12,697.05.
The government on Wednesday approved a Production-Linked Incentive (PLI) scheme for ten key sectors, including telecom, automobiles and pharmaceuticals, taking the total outlay for such incentives to nearly Rs 2 lakh crore over a five-year period.
Finance Minister Nirmala Sitharaman is scheduled to address the media later in the day.
"The yield on the 10-year benchmark bond has gradually been inching higher on account of higher US treasury yields and higher crude prices. The Reserve Bank of India shall conduct Rs 10,000-crore operation twist today," Goenka added.
Foreign institutional investors were net buyers in the capital market as they purchased shares worth Rs 6,207.19 crore on a net basis on Wednesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 0.18 per cent to USD 43.88 per barrel.
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