Benchmark indices started the trade on a positive note on Tuesday, extending their previous day gain in line with the strength in majority of Asian markets and buying in index major Reliance Industries.
The BSE Sensex climbed 320.69 points to 59,566.67 in early trade. The NSE Nifty went higher by 98.85 points to 17,764.65.
From the Sensex pack, Power Grid, NTPC, Bharti Airtel, Reliance Industries, Titan, Maruti, HDFC Bank, Hindustan Unilever and Bajaj Finance were among major gainers in initial trade.
In contrast, Kotak Mahindra Bank, Nestle, Tech Mahindra, Wipro, Sun Pharma, Tata Consultancy Services, HCL Technologies and Bajaj Finserv were among laggards.
Elsewhere in Asia, markets in Seoul, Tokyo and Shanghai were trading in the green, while Hong Kong quoted lower in mid-session deals.
The U.S. markets were closed on Monday.
The BSE benchmark jumped 442.65 points or 0.75% to settle at 59,245.98 on Monday. The Nifty advanced 126.35 points or 0.72% to 17,665.80.
"The resilience of the domestic market even in the context of strong global headwinds is a bit surprising. Clearly, India is outperforming the rest of the world," said V K Vijayakumar, Chief Investment Strategist at Geojit Financial Services.
Meanwhile, the international oil benchmark Brent crude declined 0.77% to $95 per barrel.
Foreign institutional investors (FIIs) offloaded shares worth ₹811.75 crore on Monday, as per exchange data.