Realty and banking stocks mainly saw action followed by power, capital goods, auto, oil&gas, metal, healthcare, IT and teck sectors.
The second-line mid-cap and small-cap shares too supported the sentiments.
The BSE Sensex resumed gap-up at 26,130.36 and rallied to 26,430.78. The index was quoting 26,397.31 at 1110 hours, a gain of 433.34 points or 1.67 per cent.
The 50-share Nifty was also up by 132.20 points or 1.67 per cent at 8,031.35.
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Asian markets were trading higher after the Federal Reserve cited concerns about global economic growth in its decision to hold off on raising interest rates.
China's Shanghai Composite, South Korea, Hong Kong, Singapore and Indonesia were trading higher in the range 0.40 per cent to 0.77 per cent.
However, Japan stocks trading lower by 1.44 pct.