Shares in the other Asian markets rose, taking positive cues from Wall Street where shares ended nearly 2 per cent higher on Friday.
Bharti Airtel, ITC Limited and the National Thermal Power Corporation were the top gainers in the two indices.
However, later it gave up some of the gains but still ended up by 610.55 points, or 1.83 per cent, at one-week high of 33,917.94.
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Equity markets on Monday turned encouragingly buoyant as Sensex posted its biggest gain in intra-day trade since March 2016.
On the NSE, the wider Nifty50 edged higher by 165.70 points, or 1.62 per cent, to trade at 10,392.55 points.
"Firm global cues and expectation of ease in domestic inflation to 4.74% excited investors to utilise the bargain opportunity".
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However, analysts said that Indian markets will focus on key macro data expected to be released this week.
However, shares of Karnataka Bank (down 0.39 per cent) and South Indian Bank (down 0.20 per cent) were slightly down around that time.
Crude check: Brent crude, the benchmark for more than half the world's oil, gained 0.46 percent at $65.79 per barrel while the West Texas Intermediate crude advanced 0.35 percent at $62.26 a barrel, on Monday morning. The Nifty Midcap index was up 1 percent despite balanced market breadth.
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"Asian stocks boosted sentiment on the domestic bourses while global stocks gained as worldwide trade-war concerns abated and were replaced by economic optimism following a stronger U.S. jobs report released over the weekend", Karthikraj Lakshmanan, Senior Fund Manager - Equities, BNP Paribas Mutual Fund said.