The 30-share BSE Sensex climbed 334.32 points to 57,963.27 in early trade. The broader NSE Nifty advanced 94.9 points to 17,083.30.
In Asia, the Seoul, Hong Kong and Shanghai markets were trading higher. The US markets had ended in positive territory on Monday.
"A sharp rebound in the overnight US markets could buoy local market sentiment in early trade on Tuesday in the backdrop of US banking concerns, which are seen subsiding," Prashanth Tapse, Senior VP (Research), Mehta Equities Ltd, said in his pre-market opening quote.
The BSE benchmark had declined 360.95 points or 0.62 per cent to settle at 57,628.95 on Monday. The Nifty fell 111.65 points or 0.65 per cent to settle at 16,988.40.
"Tomorrow's Fed decision and commentary will be crucial," said V K Vijayakumar, Chief Investment Strategist at Geojit Financial Services.
Meanwhile, global oil benchmark Brent crude declined 1.03 per cent to $73.03 per barrel.
Foreign Portfolio Investors offloaded equities worth Rs 2,545.87 crore on Monday, according to exchange data.