The Nifty is up 0.25 percent after rising 0.5 percent to a record high of 7,791.4, its third consecutive all-time high in as many sessions. The Sensex is up 0.44 percent after rising as much as 0.6 percent to an all-time high of 26,116.73, surpassing the 26,000 point barrier for the first time.
Software exporters lead gains ahead of Infosys Ltd's April-June earnings results on Friday. Infosys is up 2.6 percent, while Tata Consultancy Services Ltd gains 2.3 percent.
Shares in IDFC Ltd gain 6.1 percent after Morgan Stanley upgrades the stock to "overweight" from "underweight", citing its underperformance this year despite "good management, strong balance sheet, and diversified financial presence."
However, gains are limited as some blue-chips fall on profit-taking. State Bank of India falls 0.8 percent while Oil and Natural Gas Corp is down 1.4 percent.