The 30-share BSE Sensex went up 84.35 points, or 0.23 per cent, to 35,567.82. The gauge had gained 39.80 points in the previous session.
Optimistic buying in blue-chip stocks ahead of IIP data for April and CPI inflation for May, to be released after market closing on Tuesday, lifted stocks higher, brokers said.
All the sectoral indices led by healthcare, consumer durables, oil and gas, banking and auto were in the green, with gains of up to 0.84 per cent.
The NSE Nifty recaptured the key 10,800-level by rising 29.85 points, or 0.27 per cent, to 10,816.80.
Prominent gainers were Dr Reddy's, Wipro, Adani Ports, M&M, Bharti Airtel, Tata Motors, SBI, IndusInd Bank,ITC Ltd, Sun Pharma, L&T, TCS and Asian Paints, rising by up to 1.80 per cent.
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Brokers said besides unabated buying by domestic institutional investors (DIIs), a firm trend at other Asian markets influenced sentiments though investors were cautious as the historic summit between the US and North Korea got underway in Singapore.
DIIs bought shares worth a net Rs 1,062.82 crore, while foreign portfolio investors sold equities to the tune of Rs 1,156.77 crore yesterday, as per provisional data.
Globally, Hong Kong's Hang Seng rose 0.41 per cent, Japan's Nikkei gained 0.39 per cent, while China's main Shanghai Composite Index advanced 0.39 per cent.
The US Dow Jones Industrial Average ended flat on Monday.