The Ministry of Communications and Information Technology has asked the social media giant for a report by April 7.
The ministry has listed questions for Facebook, which include - whether the personal data of Indian voters and users has been compromised by Cambridge Analytica and whether agencies using Facebook data were "engaged by any entities to manipulate the Indian electoral process".
Last Friday, the government had sent a notice asking for details relating to the data breach to Cambridge Analytica.
The latest letter comes on the back of new details given by a whistleblower on Cambridge Analytica's work in India. According to details provided by Christopher Wylie, the firm did election-related analysis for many parties in India and also provided caste analysis for "a national party" and the Janata Dal United.
Last week, IT minister Ravi Shankar Prasad had warned Facebook of action, saying that the company's largest market outside the US was India. "Mr Mark Zuckerberg, you better note the observation of the IT Minister of India. We welcome Facebook in India, but if any data theft of Indians is done through the collusion of Facebook system, it shall not be tolerated. We have got stringent power in the IT Act, we shall use it, including summoning you in India," he said.
Mark Zuckerberg also said in an interview that Facebook was committed to stopping interference in elections in India.