The meeting was a courtesy call by Mistry, according to sources.
The Modi government, which was sworn in on May 26, has identified as "paramount" the need to put the Indian economy back on track.
Tata Group Chairman Emeritus Ratan Tata and his successor at the salt-to-software group Mistry, who had been invited to the swearing in, were unable to attend as they were travelling abroad.
Mistry took over as head of the USD 96.79 billion diversified conglomerate in December 2012.
In order to usher the Indian economy into a high growth path, the government had stated that it would work to rein in inflation, reignite the investment cycle, accelerate job creation and restore the confidence of the domestic and international community.
Ahead of the Budget, industry leaders met Finance Minister Arun Jaitley last week, pitching for a conducive tax environment and a bold statement of economic reforms with a view to revive investor sentiment and promote growth.
India's economic growth remained below the 5 per cent mark for the second year in a row at 4.7 per cent in 2013-14. Industry has expressed hope of a rebound with a stable government headed by Modi, who is considered pro-business.