The index recorded its ninth rise in last 10 sessions due to short-covering from operators in view of the last day of the futures and options June contract.
Crisis was seen intensifying in Greece after the nation and its international credit were far away from a deal to avert a default.
Meanwhile, launching Atal Mission for Rejuvenation and Urban Transformation (AMRUT), Smart Cities Mission, and Housing for All, Modi said urbanisation should be viewed as an opportunity and urban centres as growth engines.
"...Announcement of three flagship schemes related to housing tops a bright day for equity market," said Anand James, Co Head Technical Research Desk at Geojit BNP Paribas.
The Sensex resumed lower at 27,660.22 and dropped further to 27,635.76 on initial selling pressure. However, it recovered later to 27,968.75 on fresh buying before ending at one-month high of 27,895.97, showing a gain of 166.30 points or 0.60 per cent.
Yesterday, the Sensex had dropped by 75 points.
Shares of capital goods, realty, power, auto and refinery sectors were the major gainers of the day.
In overseas stock markets, Asian stocks ended lower, with key indices in China, Japan, Hong Kong, Singapore and South Korea dropping by 0.02 to 3.46 per cent, while Taiwan's index finished higher by 0.84 per cent.
European markets were trading lower as key indices from France, Germany and the UK moved down between 0.01 and 0.21 per cent.
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