The Sensex was trading at 48,455.13, showing a rise of 505.13 points or 1.05 per cent in opening deals; while the broader Nifty was trading higher by 150.20 points or 1.05 per cent at 14,509.65.
On the Sensex, barring three IT stocks -- HCL Tech, Tech Mahindra and TCS -- all shares were trading in the green.
On Monday, the BSE Sensex had nosedived 882.61 points or 1.81 per cent, and the NSE Nifty had plunged 258.40 points or 1.77 per cent.
Foreign institutional investors (FIIs) were net sellers in the capital markets on Monday to the tune of Rs 1,633.70 crore, according to exchange data.
"The government's decision to open up vaccination for all above 18 from May 1, and announcement of measures to incentivise vaccine manufacturers are steps in the right direction.
"This is positive from the market perspective. The market is likely to ignore the stress in the healthcare system and the pains from the second wave," V K Vijayakumar, Chief Investment Strategist at Geojit Financial Services, said.
Elsewhere in Asia on Tuesday, equity bourses saw mixed trading till afternoon as investors awaited the release of China's latest benchmark lending rate. Japan led losses among the region’s major markets, followed by Hong Kong; while South Korea and China were trading higher.
US stocks ended lower on Monday, slipping from last week's record levels, as investors awaited guidance from first-quarter earnings.
Meanwhile, global crude oil benchmark Brent futures rose 0.77 per cent to USD 67.68 per barrel on Monday, despite concerns about the impact on oil demand going forward due to rising coronavirus cases in India.