The Prime Minister said on his Facebook page that he had a very fruitful meeting with Sandberg, who called on Modi to discuss her ideas about connectivity.
Modi, describing himself as an avid user of social media, said on his page that "a platform such as Facebook can be used for governance and better interaction between the people and governments. I also talked about how Facebook can be used to bring more tourists to India."
Sandberg is on her first visit to India after becoming COO of the world's most popular social networking site.
"He told us how he believes that direct communication with people all over the world is critical to effective governance and he plans to continue using Facebook and other social media to communicate with the people of India and the world," she wrote on her Facebook page after the meeting.
Digital diplomacy can change national and international dialogues and that is why Modi "plans to champion the free and open Internet on the world stage," she wrote in her post.
Sandberg, who is on a five-day visit, met Modi along with Facebook's Global Public Policy Vice President Marne Levine and India Head of Public Policy Ankhi Das.
She had visited India in 1991 as part of a World Bank health initiative and said it was "special" to be back here.
During her visit, she met small and medium enterprises and large businesses to discuss opportunities to leverage Facebook as an important business tool.
She is scheduled to meet Communications and IT Minister Ravi Shankar Prasad this afternoon.
"India is important to the global economy, as well as to Facebook, and we look forward to working together on internet.Org to bring the next billion people online," she said.
Sandberg added that access to the Internet would create more economic, social and political opportunities for the people of India.