Shares of consumer durable, power, metal, IT, healthcare and realty sectors were in good demand.
The BSE-30 share barometer Sensex resumed higher at 18,602.56 and moved up further to a high of 18,728.19 before quoting 18,701.18 points at 1030 hours.
It showed a gain of 181.74 points or 0.98 per cent from its last last weekend's level.
The NSE 50-share index, Nifty, also rose by 47.40 points or 0.87 per cent to 5,519.15 at 1030 hours.
The market may remain volatile this week ahead of the expiry of futures & options (F&O) August contract on coming Thursday.
Asian stocks rose for a second day in their early trade after a slump in US home sales eased speculation that the Federal Reserve will reduce economic stimulus next month.
Key indices in Singapore, Hong Kong, China, Japan, Taiwan and South Korea were up by 0.14 to 1.41 per cent.
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