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The weak start to the year comes ahead of key events later this month, including inflation data due mid-month that will help determine whether the Reserve Bank of India raises interest rates at its policy review on January 28.
The RBI has made clear it could resume tightening monetary policy after two rate hikes last year even as economic growth slows.
The HSBC Manufacturing Purchasing Managers' Index (PMI), compiled by Markit, fell to 50.7 in December from 51.3 in the previous month, showing India's factories lost momentum although input prices eased lightly.
"Good and consistent demand from state-run banks, may be on account of genuine oil demand, and a fall in shares took (USD/INR) spot higher," said Ashish Barua, associate vice president at IndusInd Bank.
The partially convertible rupee closed at 62.26/27 per dollar compared with 61.91/92 on Wednesday. It fell to 62.28 in session, its lowest since December 20.
The falls came after the benchmark Sensex ended down 1.2 percent, as investors booked profits on blue chips. <.BO>
Dealers said dollar demand from a petrochemical company and buying by state-run banks, largely to meet needs of oil refiners, also put pressure on the rupee, pushing it past 62 to a dollar.
A breach of 62.10 to the dollar led to short-covering, they said.
In the offshore non-deliverable forwards, the one-month contract was at 62.69, while the three-month was at 63.55.
(Editing by Sunil Nair)
