Allegations that Indian Prime Minister Narendra Modi's official mobile application was sending personal user data to a third party without their consent caused a furore on social media in India and drew criticism from the leader of the main opposition party on Sunday.

Modi's ruling Bharatiya Janata Party denied the allegations and said the data was being used only for analytics to offer all users the "most contextual content".

A security researcher, who has previously highlighted some vulnerabilities in India's national identity card project and who tweets under the pseudonym Elliot Alderson, posted a series of tweets on Saturday stating the app was sending personal user data to a third-party domain that was traced to an American company.

The tweets, which come at a time of heightened sensitivity around the alleged misuse of personal data amid the unfolding Facebook-Cambridge Analytica, triggered a stir in India on social media.

"Hi! My name is Narendra Modi. I am India's Prime Minister. When you sign up for my official App, I give all your data to my friends in American companies," wrote opposition Congress Party Chief Rahul Gandhi in a Twitter message on Sunday.

The BJP quickly responded on Twitter, saying Gandhi was trying to divert attention. The BJP has accused the Congress of engaging Cambridge Analytica in India, a charge the opposition party has denied.

Alderson, who initially pointed out that the Narendra Modi app was sharing data with a third party without the consent of users, earlier on Sunday posted a new tweet saying the app had "quietly" updated its privacy policy after his previous tweets.

Reuters could not independently verify Alderson's claim.

Prime Minister Modi has not commented on the issue.

BJP said the app - which has seen about 5 million downloads on the Google Android Play Store - allows users access even in a guest mode that does not require them to grant any permissions.

"The permissions required are all ... cause-specific," the BJP tweeted.