The NSE, or Nifty 50, rose 0.45 percent to a record high of 10,011.30, then pared some of the gains and was up 0.06 percent by 11.15 am.
The benchmark BSE Sensex advanced as much as 0.40 percent to a record high of 32,374.30 points.
The NSE has surged 22 percent this year, just behind South Korea's and Hong Kong's markets, in a broad-based rally fuelled by a surge in foreign investments and flows from retail investors buying into mutual funds for the first time.
Both investors have bet heavily that economic growth will accelerate from 6.1 percent in the January-March quarter, boosting corporate earnings. Hopes are also high for economic and fiscal reforms after the government unveiled a national goods and services tax this month.
Still, valuation concerns linger: the NSE was trading at around 21 times 12-month forward price-to-earnings, compared with a five-year average of 17.91.
"It is a historical moment given Nifty touched the key psychological mark," said Siddhartha Khemka, Head Research for Equity for Centrum Wealth.
"However we can expect a consolidation at higher levels given the rich valuations towards the end of the current corporate results season," he added.
Among the top gainers on Tuesday were HDFC Bank which rose as much as 1.4 percent after posting solid results on Monday, prompting Morgan Stanley and Jefferies to upgrade their ratings.
Bharti Infratel rose 2.2 percent, even after the telecom tower infrastructure provider missed first quarter estimates on Monday, as net tenancy additions and EBITDA margin surged.
An extension of the rally in the near term will probably depend on the outcome of earnings of India's blue chips, with the bulk of results yet to be released. Besides, not all analysts are convinced of a recovery as a dearth of private investments risks hampering growth.
"In the medium term, we are not very positive about the market because of high valuations and a muted outlook for the current corporate results season," said Vinod Nair, Head of Research at Geojit Financial Services.
But most analysts agree that prospects are brighter over the long-term, as retail investors continue to invest into mutual funds via regular monthly contribution.
Deutsche Bank estimates retail investors have ploughed a record $31 billion into Indian equities through mutual funds since May 2014, more than the estimated $21 billion overall by foreign investors over the same period.
($1 = Rs 64.37)