The S&P BSE Sensex benchmark index rose as much as 65.15 points in early trade to 38,961.86, and the NSE Nifty index moved 10.65 points higher to 11,599.00, compared with its previous close of 11,588.35.
Advances in metal, banks and energy counters supported the markets however weakness in auto and IT stocks limited the upside. Analysts say corporate earnings from large cap companies due this week will be watched closely for market cues.
At 9:21 am, the Sensex traded 12.52 points - or 0.03 per cent - higher at 38,909.23, while the Nifty was up 2.80 points - or 0.02 per cent - at 11,591.15.
Top percentage gainers on the 50-scrip index at the time were ONGC, Indian Oil, Cipla and Yes Bank, trading between 0.80 per cent and 1.36 per cent higher. On the other hand, Indiabulls Housing Finance, Mahindra & Mahindra, TCS and Zee Entertainment - trading between 0.94 per cent and 3.08 per cent - lower were the top laggards.
While Reliance Industries, Infosys and HDFC Bank contributed the most to the advances in Sensex, TCS, Kotak Bank and Mahindra & Mahindra were the top drags.
The Sensex and Nifty had closed 0.41 per cent and 0.31 per cent higher respectively on Monday.
Official data showed on Monday that wholesale inflation - gauged by the Wholesale Price Index (WPI) - hit a 23-month low of 2.02 per cent in June, helped by a decline in the prices of vegetable, fuel and power.
Meanwhile, consumer inflation picked up to 3.18 per cent last month, marking the highest level recorded since October 2018, according to separate data released last week.
Equities in other Asian markets inched up on Tuesday, with MSCI's broadest index of Asia-Pacific shares outside Japan trading 0.04 per cent higher. Australian shares were up 0.1 per cent and Japan's Nikkei stock index dipped 0.36 per cent.
Investors were relieved by encouraging Chinese economic data on the previous day, though broad pressure across global business and investment from Sino-U.S. trade frictions and slowing world growth reinforced expectations of policy easing by major central banks.
Overnight on Wall Street, the Dow Jones Industrial Average, the S&P 500 and the Nasdaq Composite benchmark indexes added 0.1 per cent, 0.02 per cent and 0.17 per cent respectively.
US S&P 500 e-mini stock futures pointed up, rising 0.07 per cent in early Asian trade.