The benchmark indices which jumped up over 1 per cent each in the opening session, extended their gains by mid-morning on Tuesday.
At 11:23 am, Sensex was up 689 points or 1.39 per cent at 50,269. The NSE Nifty rose 203 points or 1.36 per cent to trade at 15,126.
The top gainers on the Sensex were Bajaj Finance, Power Grid, Titan, Bajaj Auto and HDFC Bank. There were only two stocks in the red, namely, Bharti Airtel and ITC.
According to a PTI report, Sensex soared over 600 points in early trade led by gains in index majors HDFC twins, ICICI Bank and Infosys amid a positive trend in global markets.
In the previous session, Sensex zoomed 848.18 points or 1.74 per cent to end at 49,580.73; and Nifty surged 245.35 points or 1.67 per cent to settle at 14,923.15.
Foreign institutional investors (FIIs) were net sellers in the capital market as they offloaded shares worth Rs 2,255.84 crore on Monday, as per provisional exchange data.
The report quoting V K Vijayakumar, Chief Investment Strategist at Geojit Financial Services, said the positive trigger for the market now is the steadily declining fresh Covid cases and the steadily rising recovery rates.
"The latest numbers (2.62 lakh fresh cases and 4.22 lakh recoveries) indicate a continuation of this positive trend. The market is discounting progressive lifting of the widespread lockdowns starting in early June. Even though growth and earnings will be impacted in Q1, smart recovery can be expected in the subsequent quarters," he said.
Elsewhere in Asia, bourses in Shanghai, Hong Kong, Tokyo and Seoul were trading on a positive note in mid-session deals.
Equities on Wall Street ended with losses in overnight trade.
Meanwhile, international oil benchmark Brent crude was trading 0.39 per cent higher at $69.73 per barrel.