Coming off a holiday, the rupee traded at 81.58 per dollar by 11:12 a.m. IST, against its previous close of 81.59. The local unit is headed for a weekly loss after two straight weeks of gains.

Custodial banks are on the bid on USD/INR, likely on behalf of their clients, a trader at a private bank said. There was also fix-related dollar demand, another dealer said.

"The rupee could be seen experiencing bearishness on the back of Indian bourses trading in the red and continued withdrawal of funds by foreign institutional investors," said Ritesh Bhansali, vice-president at Mecklai Financial Services.

"The currency is expected to trade in the range of 81.40- 81.80."

Even as Asian shares rallied, Indian stocks were down 1%, extending losses from Wednesday after U.S. short-seller Hindenburg Research's scathing attack on conglomerate Adani Group sparked a selloff in group stocks.

Foreign investors offloaded $292 million worth of Indian shares on a net basis on Wednesday, preliminary exchange data showed.

Meanwhile, the dollar index was up 0.2%, heading towards 102-levels. Data overnight showed the U.S. economy expanded at a faster pace than expected in the December quarter.

Meanwhile, the U.S. core personal consumption expenditure (PCE), the Fed's preferred inflation measure, eased to 3.9% in the December quarter, from 4.7% in the prior quarter.

Relief on inflation could push the Fed to opt for a smaller 25-basis-points (bps) rate hike next week. However, analysts reckon the Fed will continue to signal that more rate hikes are likely.

Market participants are also awaiting India's Union budget due to be presented on Feb. 1. The government will likely borrow a record 16 trillion rupees in the fiscal year ending March 2024, according to a Reuters poll of economists.

(Reporting by Anushka Trivedi; Editing by Dhanya Ann Thoppil)

By Anushka Trivedi