The BSE gauge Sensex closed 692.79 points or 2.67 per cent higher at 26,674.03, after a highly volatile trading session. The index swung between a high of 27,462.87 and a low of 25,638.90 during the day.
Likewise, the NSE barometer Nifty settled 190.80 points, or 2.51 per cent, up at 7,801.05.
Both Sensex and Nifty had suffered their worst ever single-session drop in history on Monday. Indices had closed with up to 13 per cent plunge.
On Tuesday, Indian equities followed an improved investor sentiment in Asia after the Federal Reserve announced limitless bond-buying programme to support the US economy.
Top gainers in the Sensex pack included Infosys, Bajaj Finance, HUL, Maruti, HCL Tech and Reliance Industries; while M&M, IndusInd Bank, ITC, PowerGrid and L&T were among the losers.
Sectorally, BSE IT, teck, energy, FMCG, auto, bankex, finance and metal indices advanced up to 6.95 per cent.
While realty, capital goods and basic materials indices ended up to 2.01 per cent lower.
In the broader market, BSE midcap and smallcap indices rose up to 1.56 per cent.
"Market seemed to breathe a sigh of relief today after the crash yesterday, in sync with the global markets. In addition to the huge relief package by the US Fed yesterday, there were also expectations of a fiscal package by the government," Vinod Nair, Head of Research at Geojit Financial Services, said.
The market came off its highs after no significant announcements by the finance minister and the fact that the economic package was still in development, he said, adding that European and US manufacturing activity data due later, which may indicate the impact of Covid-19 on economies, could influence markets tomorrow.
With the coronavirus lockdown hitting the Indian industry hard and causing job losses, Finance Minister Nirmala Sitharaman said an economic package to help tide over the crisis will be announced very soon.
Sitharaman told reporters an announcement on the package would be made sooner than later.
On volatility in stocks, she said regulators and her ministry are monitoring developments and volatility in markets.
According to experts, a major package from the government of India and the Reserve Bank is expected shortly, and the market is likely to remain hugely volatile with rising possibility of V shaped recovery occasionally.
The US Fed is now leading from the front with its historic package which includes open-ended purchase of securities, direct loans to companies, purchase of corporate bonds, lending against student loans and credit card loans, they said.
The Federal Reserve on Monday announced it will buy unlimited amounts of US Treasury debt -- essentially printing money for the economy -- as well as new steps to lend directly to small- and medium-sized companies that have been among the hardest-hit as economic activity dries up.
Other central banks are also expected to follow suit with bold measures to ease the severely strained credit and financial markets, experts noted.
Traders said extreme lockdown measures taken by the government of India and authorities across the world still weigh on global investor sentiment.
Bourses in Shanghai, Hong Kong, Tokyo and Seoul rallied up to 8 per cent. Exchanges in Europetoo rallied up to 6 per cent.
Meanwhile, the Indian rupee appreciated against the US dollar to trade 26 paise higher at 75.94.
Global crude benchmark, Brent crude futures rose 5.22 per cent to USD 28.44 per barrel.
Coronavirus cases in India crossed 500 and one more death from the infection reported taking the toll to ten, as the Centre on Tuesday asked the states and union territories to clamp curfew wherever necessary in the wake of people defying lockdown orders in several parts of the country.
The number of global Covid-19 infections has shot past 3,80,000. Worldwide fatalities topped 16,500. ANS MKJ