At 11:30AM, the 30-share Sensex was up 38 points at 20,813 and the 50-share Nifty was up 12 points at 6,199.
The HSBC Services Purchasing Managers' Index (PMI), compiled by Markit, fell to 46.7 in December from 47.2 in November.
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New orders index dropped to 47.3 in December from 48.2 in November, and has also remained below the 50 mark for six months.
Asian stocks were down tracking China's weak December services PMI. Shares in Japan witnessed profit taking after recent gains while a stronger yen also dampened sentiment. According to a survey by China's National Bureau of Statistics growth in the services sector slipped to a four-month low of 54.6 in December compared with 56.0 in November.The Nikkei was down 2.4%, the Shanghai Composite slipped 1.8%, Hang Seng was down 0.7% and Straits Times was trading marginally lower.
The rupee continued to remain weak due to dollar demand by importers. The rupee may weaken further during the day, according to currency dealers. They also said the RBI may intervene if that happens. The Indian currency was trading at 62.27 compared with Friday's close of Rs 62.16.
Profit taking was seen in index heavyweights with ICICI Bank, Reliance Ind, Infosys and SBI down 0.6-1.6% each.
TCS was marginally down amid profit taking after recent gains.
State-owned Oil and Natural Gas Corp (ONGC) was up nearly 3% after the company said it will invest around $9 billion in bringing to production an array of oil and gas discoveries in its prolific Krishna-Godavari basin block off the east coast by 2017-18.
Tata Motors also rebounded today after the recent correction following dismal December sales. The stock was up 1.4%.
Other gainers include, L&T, ITC and Maruti Suzuki.
Among other shares, Shares media companies are in demand and trading higher by up to 7% in otherwise weak market on hopes that the year 2014 turn to be a good year for the entire sector including television, radio, digital and print media.
Entertainment Network (India), TV18 Broadcast, Network18 Media and Investments, TV Today Network and NDTV were up 5-7% on the BSE.
JSW Steel was trading higher by 4% at Rs 1,034 after the company said that Raigad Unit of Heidelberg Cement India has been transferred to the company with effect from the end of business hours on January 3, 2014.
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