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, 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.
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