The fresh trade war tensions along with unabated foreign fund outflows weighed heavily on the market sentiments, traders said.
The 30-share BSE gauge closed marginally higher by 8.36 points or 0.02 per cent at 40,802.17.
The 30-share index was trading 81.65 points, or 0.20 per cent, higher at 40,875.46.
PMI data for manufacturing and services sectors are scheduled to come this week which may also impact trading at the bourses.
The 30-share Sensex pared some losses, ending 336.36 points or 0.82 per cent lower at 40,793.81.
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.
The 30-share Sensex was trading 207.41 points, or 0.51 per cent, higher at 41,028.71 in morning session.