The Sensex index rose as much as 254.83 points in early deals to 39,649.47, and the NSE Nifty benchmark climbed to 11,860.85, up 72 points from the previous close.
Buying was seen across sectors by banking, auto and metal shares. Analysts say any major announcements in the upcoming Budget will be monitored closely.
At 10:19 am, the Sensex traded 188 points - or 0.48 per cent - higher at 39,582 while the Nifty was up 56 points - or 0.48 per cent - at 11,845.
Top gainers on the 50-scrip index at the time were NTPC, Indiabulls Housing Finance, Dr Reddy's, Tata Steel, Zee Entertainment, Eicher Motors and IndusInd Bank, trading between 1.33 per cent and 1.95 per cent higher.
HDFC Bank, ICICI Bank and Axis Bank contributed the most to the advances in Sensex.
Market breadth favoured gains, with 825 stocks on the BSE trading in the positive zone and 329 struggling with losses. On the NSE, 1,021 stocks advanced while 489 declined.
The Nifty Bank - a sectoral index on the NSE comprising banking stocks - rose as much as 0.77 per cent. The index finished June with a fall of 0.86 per cent.
Aviation stocks were in focus after oil marketing companies reduced jet fuel prices by 5-6 per cent. SpiceJet shares rose as much as 3.08 while IndiGo went up 1.49 per cent in intraday trade.
Equities in other Asian markets rallied while bonds retreated amid easing concerns on the US-China trade front.
MSCI's broadest index of Asia-Pacific shares outside Japan added 0.4 per cent, and Japan's Nikkei climbed 1.6 per cent to a two-month top. Chinese blue chips climbed 2.1 per cent to their highest since late April. E-Mini futures for the S&P 500 rose 0.8 per cent and FTSE futures 0.5 per cent.
The US and China agreed on Saturday to restart trade talks after US President Donald Trump offered concessions to his Chinese counterpart Xi Jinping when the two met at the sidelines of the G20 summit in Japan over the weekend. These included no new tariffs and an easing of restrictions on tech company Huawei in order to reduce tensions with Beijing.
The Sensex and Nifty had ended 0.48 per cent and 0.45 per cent lower respectively on Friday, declining for a second consecutive session.