The broader NSE Nifty all-time high above 6,500 points, although the benchmark BSE Sensex got there first, hitting a record high on Thursday and again on Friday.
Foreign investors are driving the rally, sparking strong gains in the rupee as well.
On Thursday foreign investors posted their biggest daily purchases since December 19, amounting to a net 12.73 billion rupees, and marking a 15th consecutive buying session.
The strong buying is confounding expectations that foreign investors would turn cautious ahead of general elections due to start on April 7.
Instead, analysts say foreign investors are switching from exporters, which had attracted the bulk of overseas buying last year, to domestic-focused sectors in a more direct bet on India's own outlook.
"One-way buying by overseas investors is supporting the gains. We expect sectors, which are connected to the core economy such as infrastructure, capital goods and metals are likely to see more buying interest (from foreign investors)," said Suresh Parmar, head of institutional equities at KJMC Capital Markets.
The BSE Sensex and Nifty were up 1.2 percent at 11.59 a.m. The Sensex earlier touched a record high of 21866.51 points.
For the year, foreign investors remain net buyers of $850 million worth of shares, after a wobbly share performance in January had sparked some selling, after buying about $20 billion worth last year.
Overseas investors have also turned into strong buyers of debt, with net purchases of $4.9 billion so far this year, helping partly reverse their net sales of $8 billion in debt in 2013.
The strong buying is a stark turnaround from last year when the country was struggling to contain a record-high current account deficit, sending the rupee to a record low of 68.85 to the dollar in late August.
However, strong curbs on gold imports imposed by the government, including a 10 percent duty, has helped narrow the current account deficit, leading to a more stable currency.
The rupee reached up to 60.95 to the dollar, its strongest level since December 9.
Domestic-focused lenders were among the top gainers on Friday.
ICICI Bank, the country's biggest private sector lender, surged 6.75 percent, while State Bank of India rose 4.7 percent.
Meanwhile, Larsen & Toubro Ltd, India's biggest engineering and construction firm, surged nearly 6 percent.
However, exporters fell on Friday, with Tata Consultancy Services (TCS) down 2.7 percent, a reversal of a trend in which foreign investors had bet big on drugmakers and software services exporters last year.