After touching an all-time high of 61,894.33 in opening deals, the 30-share Sensex was trading 511.54 points or 0.83 per cent higher at 61,817.49.
Similarly, the Nifty surged 157.40 points or 0.86 per cent to 18,495.95. It touched a new intra-day record of 18,521.10 in initial deals.
Infosys was the top gainer in the Sensex pack, rising over 2 per cent, followed by Tata Steel, HDFC Bank, ICICI Bank, Titan and IndusInd Bank.
On the other hand, Asian Paints, Bajaj Auto, Dr Reddy's and HCL Tech were trading with losses in early deals.
In the previous session on Thursday, the 30-share index settled 568.90 points or 0.94 per cent higher at 61,305.95, and the Nifty surged 176.80 points or 0.97 per cent to a new lifetime closing high of 18,338.55.
Foreign institutional investors (FIIs) were net buyers in the capital market, as they purchased shares worth Rs 1,681.60 crore, as per exchange data.
Market remained shut on Friday on account of Dussehra'.
Elsewhere in Asia, bourses in Hong Kong, Shanghai and Tokyo were trading with losses in mid-session deals, while Seoul was positive.
Meanwhile, international oil benchmark Brent crude rose 1.07 per cent to USD 85.77 per barrel.