The issues discussed included 'Swachh Bharat' Mission with the Facebook co-founder.
Zuckerberg, who called on the Prime Minister, expressed his interest in working with the government in the areas of healthcare and education.
The Prime Minister pointed out that lots of terrorist elements are using social media platforms to recruit members, according to an official statement.
"This is unfortunate and we need to think of the role the social media can play to stop terror," Modi said.
Facebook will extend help in developing the Clean India Mobile App that would be launched soon.
"This would give a strong impetus to the Swachh Bharat Mission," the statement said.
They discussed a wide range of issues revolving around the innovative use of Facebook as a platform to engage with a large audience in the service of humanity, the statement said.
They also talked about the Digital India initiative and the Prime Minister asked Zuckerberg to identify some domains of Digital India where Facebook can get involved and help.
Facebook chief said that he is extremely excited about the Digital India initiative of the Government of India.
Modi recalled how he used social media during campaigns such as tracking the missing children, during his tenure as Chief Minister of Gujarat and how it gave wonderful results.
The Prime Minister appealed to Zuckerberg to promote India's rich tourism potential through Facebook.
He asked Facebook to look at how to enhance Internet literacy along with Internet connectivity.
Earlier in the day, the Facebook CEO met Telecom and IT Minister Ravi Shankar Prasad.
Zuckerberg is the third high-profile CEO of a US-based firm, after Amazon's Jeff Bezos and Microsoft's Satya Nadella, to visit India in last few days.
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