"Ginni Rometty, CEO, IBM, calling on PM Shri @narendramodi," Press Information Bureau tweeted with picture of Modi and Rometty without disclosing details of discussions between them.
Rometty is on a three-day visit to India and has met senior leaders in the government as well as from the industry.
IBM CEO has expressed optimism for India citing strong GDP growth, expanding base of startups and growing trend of new technologies like cloud in the country.
"I say this century, the 21st century is Indian century... I am very optimistic about the tomorrow ahead and this is a fact-based optimism," she said at an event on Tuesday.