Benchmark indices extended the early gains with Nifty above 8600.
The Sensex is up 1,50 points at 29746.37, and the Nifty up 332.70 points or 4.00% at 8650.55. About 1164 shares have advanced, 329 shares declined, and 86 shares are unchanged.
Shares rose for the third straight session on Thursday, as investors awaited a domestic stimulus to fight the impact of the coronavirus outbreak on an already slowing economy, and the US Senate passed a $2 trillion virus relief bill.
Broader Asian equities rose and MSCI's broadest index of Asia-Pacific shares outside Japan was up 4.5%.
"There were some hiccups, but the US has passed the bill," said Neeraj Dewan, director at Quantum Securities in New Delhi. "Now the cry for a good domestic package is getting stronger and anticipation is building."
As the country began the second day of a three-week nationwide lockdown, the NSE Nifty 50 was 3.21 percent higher at 8,584.45 , while the S&P BSE Sensex rose 3.41 percent to 29,503.22.
The Nifty has climbed 9 percent in the last two sessions as global sentiment improved as governments considered stimulus plans, but the blue-chip index is still down some 30 percent since the start of this year as markets everywhere are pummelled by the crushing impact of the virus on business.
The US Senate on Wednesday overwhelmingly backed a $2 trillion bill aimed at helping unemployed workers and industries hurt by the coronavirus epidemic, as well as providing billions of dollars to buy urgently needed medical equipment.
Reuters reported on Wednesday that India was likely to unveil an economic stimulus package of more than 1.5 trillion rupees ($19.6 billion) to fight the pandemic-fueled downturn in the country. India was likely to announce the package by the end of the week, sources said.
The stimulus package comes as growth in Asia's third largest economy has slowed to multi-year lows, with five successive interest rate cuts by the central bank last year so far doing little to boost the economy.
The outbreak has infected over 550 people so far and killed 10, and the country is in the midst of a 21-day lockdown that has seen factories and businesses come to a halt.
Pharmaceutical and IT stocks led gains in India. The Nifty pharma index was up 2.67 percent and on track to gain for a third straight day, while the Nifty IT index climbed 4.02 percent.
IndusInd Bank, down more than 70 percent this year, was at the top of the Nifty 50 with a 15 percent advance.
Meanwhile, the rupee was stronger by 0.26 percent at 75.8450 against the dollar but still hovered around its all-time lows that it hit earlier this week.