BENGALURU, July 13 (Reuters) - Gains in banking and auto stocks lifted Indian shares on Tuesday, as a lesser-than-expected rise in June retail inflation helped put stimulus pullback worries at ease amid a rally in global stocks. As of 0505 GMT, the blue-chip NSE Nifty 50 index (.NSEI) and the benchmark S&P BSE Sensex (.BSESN) were up 0.48% each at 15,767.40 and 52,624.65 points, respectively. "Earlier there was a fear in the market that a higher rise in inflation would cause a pullback in stimulus but those worries have now been put to ease," said Saurabh Jain, assistant vice president of research at SMC Global Securities Ltd in Delhi. "The rally happening in the global market is also providing clarity as the Delta variant is not hurting markets in a major way." The Nifty realty index (.NIFTYREAL) was up 0.78% while the Nifty Infra index (.NIFTYINFR) rose 0.49%. Both indexes were set to gain for a third consecutive session and have added over 25.4% and 20.2% respectively, this year. "The rally in domestic markets is shifting towards real estate, infrastructure and capital goods which have been in the doldrums for many years," Jain said. ICICI Bank (ICBK.NS) shares rose 1.8% and HDFC Ltd (HDFC.NS) gained 1.5%. The lenders were among the top boosts to the Nifty Bank index (.NSEBANK) that added 0.61%. The Nifty Auto index (.NIFTYAUTO) was up 0.56%, helped by gains in Jaguar Land Rover parent Tata Motors (TAMO.NS), which was up 0.8%. In Mumbai trading, shares of Sunteck Realty (SUNT.NS) jumped 6.4% after the firm reported a rise in first-quarter pre-sales bookings. India"s retail inflation rose less than expected in June, strengthening the view that the central bank could keep policy rates at current levels to support an economy hit hard by COVID-19. Economists said the June inflation print was above the upper range of the central bank"s 2%-6% target, but price pressures appeared to be easing. read more Reporting by Shivani Singh in Bengaluru; editing by Vinay Dwivedi Our Standards: The Thomson Reuters Trust Principles.