At the closing bell, the 30-share BSE Sensex was lower by 70.70 points or 0.17 per cent at 40,779.59.
BSE Sensex was trading 100.56 points, lower at 40,749.73 at 1149 hours.
The 30-share BSE Sensex was trading higher by 84.17 points at 40,934.46 in n opening deals.
The 30-share BSE Sensex was down 119.42 points or 0.29 per cent to 40,556.03 in early deals.
The fresh trade war tensions along with unabated foreign fund outflows weighed heavily on the market sentiments, traders said.
PMI data for manufacturing and services sectors are scheduled to come this week which may also impact trading at the bourses.
Similarly, the broader NSE Nifty was quoting 38.45 points, or 0.32 per cent, down at 12,112.70.
After touching its lifetime high of 41,163.79 during the day, the 30-share Sensex rose by 109.56 points or 0.27 per cent.
After hitting its life-time high, Sensex pared some gains to trade 52.93 points higher at 41,073.54 in morning session.
Sensex rose by 199.31 points or 0.49 per cent to end at a new life-time high of 41,020.61 as 24 of its constituents ended in green.