The NSE Nifty 50 index was up 0.5% at 17,785.4, as of 0350 GMT, while the S&P BSE Sensex was 0.6% higher at 59,817.2. Indian markets were closed on Monday for a holiday.
India's consumer inflation dipped to 6.71% in July, aided by a slower increase in food and fuel prices. The figure was marginally lower than the 6.78% forecast by economists in a Reuters poll.
Asian stock markets struggled for direction, weighed down by worries over global growth following weak China data that knocked oil prices and commodity-linked currencies.
Banking and auto stocks gained in India, with the Nifty Auto index up 1.1%.
Shares of Life Insurance Corporation of India rose 2.5% after the country's biggest insurer posted a 20% jump in June-quarter premium income on Friday.
India's currency and debt markets remained closed on Tuesday for a holiday.
(Reporting by Tanvi Mehta in Bengaluru; Editing by Subhranshu Sahu)