Also, foreign institutional investors sold Rs 608 crore worth of index futures and Rs 18 crore of cash shares on Friday, dampening the sentiment.
Losses on Monday also tracked lower Asian shares after growth in China's services sector slowed sharply last month, raising concerns about the pace of recovery in the world's second largest economy.
For India, the HSBC Services Purchasing Managers' Index, compiled by Markit, showed a continued contraction in activity, falling to 46.7 in December from 47.2 in November as new orders dwindled, although firms hired at their fastest pace in five months.
India is due to post wholesale and consumer prices data next week, which will help determine whether the Reserve Bank of India will resume raising interest rates, after tightening monetary policy by a total of 50 basis points over September and October.
The Sensex fell 0.3 per cent, or 64.03 points, to end at 20,787.30, marking its the lowest close since December 19.
The broader Nifty lost 0.3 per cent, or 19.70 points, to end at 6,191.45, closing below the psychologically important 6,200 level.
Among the blue chip shares, ICICI Bank fell 2.4 per cent, while Reliance Industries ended down 1.1 per cent. In state-owned large cap banks, State Bank of India fell 1.8 per cent while Bank of Baroda ended 1.9 per cent lower.
Larsen and Toubro fell 0.2 per cent, losing for a fourth session, with a total decline of 5.6 per cent, on concerns that the company's new orders are slowing, dealers say.
Infosys fell 1.3 per cent after making a record high at Rs 3,580.5 on profit-taking and caution ahead of its October-December results on Friday.
Power producers fell on media reports that the government in Maharashtra is planning to cut power rates. Tata Power fell 2.6 per cent, while Reliance Infrastructure ended lower 0.5 per cent.
However, among stocks that gained, Lupin gained 0.6 per cent, adding to Friday's three per cent rise on hopes of regulatory approval for its request for permission to raise its foreign investor stake. The Foreign Investment Promotion Board is due to meet this week and dealers cite expectations the regulator could consider Lupin's proposal.
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