The S&P BSE Sensex surged as much as 962.12 points to hit 38,892.89 in early trade, and the NSE Nifty climbed to 11,694.10, up 286.95 points from the previous close. Advances in banking, financial services, auto and metalstocks supported the markets.
At 9:33 am, the Sensex traded 672.25 points - or 1.77 per cent - higher at 38,603.02, while the Nifty was up 203.05 points, or 1.78 per cent, higher at 11,610.20.
Top gainers on the 50-scrip index at the time were Indiabulls Housing Finance, Larsen & Toubro, State Bank of India, ICICI Bank, Maruti Suzuki India and Mahindra & Mahindra, trading between 3.49 per cent and 4.60 per cent higher.
Reliance Industries, ICICI Bank and HDFC contributed the most to the advances on Sensex.
Some analysts expect a rally in the markets till the election results due on Thursday.
"Any movement in the markets till election results will depend on the positions investors have taken. If there is a huge short position, a rally may be on the cards but it will be short-lived since valuations are not cheap at present," AK Prabhakar, IDBI Capital, told NDTV.
The poll of polls, an aggregate of exit polls, gives the BJP-led National Democratic Alliance (NDA) 302 of 543 seats.
"A stable government will be best for the markets," he said.
Equities in other Asian markets were steady as investors tried to catch their breath following another week of escalating trade tensions between the US and China. MSCI's broadest index of Asia-Pacific shares outside Japan tacked on 0.6 per cent in early trade, after a 3 per cent loss the previous week.
Japan's Nikkei stock index added 0.4 per cent, after data showed growth in the world's third-biggest economy unexpectedly accelerated in the first quarter. US S&P 500 e-mini futures turned higher, rising 0.5 per cent following losses on Wall Street on Friday.
The NSE Nifty had risen 128.25 points - or 1.14 per cent - last week, while the S&P BSE Sensex added 467.78 points (1.25 per cent).