The Sensex jumped 284.03 points or 0.91 percent to 31,663.58 while Nifty was up 97.55 points or 1.06 percent at 9,284.85 at 10.20 am.
It had opened at 31,646.45 and has so far touched an intra-day high of 31,646.45 and a low of 31,292.92.
On Wednesday, the Sensex ended at 31,379.55 points while Nifty50 closed at 9,187.30 points.
Meanwhile, Wall Street's major indices jumped as the investor sentiments were lifted by weakening oil concerns and expectations of relief package.
On Wednesday, the Dow Jones Industrial Average jumped 456.94 points, or 1.99 per cent, to 23,475.82. The S&P 500 rose 62.75 points, or 2.29 per cent, to 2,799.31. The Nasdaq Composite Index increased 232.15 points, or 2.81 per cent, to 8,495.38, Xinhua news agency reported.
The Sensex jumped 284.03 points or 0.91 percent to 31,663.58 while Nifty was up 97.55 points or 1.06 percent at 9,284.85 at 10.20 am.
All the 11 primary S&P 500 sectors climbed, with technology and energy up 3.87 per cent and 3.58 per cent, respectively, outpacing the rest.
Brent oil rose more than 7 per cent, after earlier in the day touching its lowest level since 1999, on the prospects of further cuts in production to reduce the glut in the oil market, sending the S&P 500 energy index up 3.6 per cent.
The West Texas Intermediate for June delivery jumped 19.1 per cent to settle at $13.78 a barrel on the New York Mercantile Exchange, following a 43.37-per cent drop in the prior session. The international benchmark Brent crude settled 5.38 per cent higher on Wednesday.
While Asian shares also saw modest gains tracking the global peers with rebound in oil prices. Stocks in Hong Kong, Tokyo and Seoul witnessed marginal gains while Chinese stocks continued to fluctuate. Futures on the S&P 500 Index were little changed after the gauge rebounded from its worst sell-off in three weeks amid quarterly results.
(With inputs from agencies)