India on Thursday vowed to strengthen its online security after high school exam papers were leaked ahead of crucial tests, forcing millions of students to resit their finals.

Education Minister Prakash Javadekar said an investigation was underway into how the mathematics and economics papers were accessed and spread via WhatsApp before the exam.

"The criminals who did this won't be spared. I am sure police will catch these people soon. Let me assure that we will further improve the system and make it foolproof," he told reporters Thursday.

It is another embarrassment for a government which has weathered storms around alleged cracks in its Aadhaar system, a database containing the personal details of more than one billion Indians.

It comes as Facebook reels from a scandal over user data and India's ruling and main opposition parties accuse each other of mining and sharing followers' personal information.

The row erupted this weekend after a French security researcher flagged flaws with Prime Minister Narendra Modi's personal app, alleging that users' data was being shared without their consent.

The main opposition Congress party's Rahul Gandhi used the exam leak to revive the attack on Modi's administration over digital security.

"2.8 million students to take exams again!! I mean is it a bloody joke? Who is accountable for this big mess?," he posted on Twitter.

The Central Board of Secondary Education papers are crucial for students hoping to secure admission to some of India's most prestigious public universities and there was widespread anger at the leak.

Javadekar said he "understood the pain and anguish and frustration" of parents and students following the breach.

Police in Delhi investigating the leak said 25 people, including students and tutors, had been questioned as part of their inquiries but no arrests made so far.

"For now, we are trying to establish the trail of this leak. Most people we have spoken with only received it on WhatsApp," said special commissioner of police RP Upadhyay.

Cheating in exams is common in India including paying large bribes to buy test papers, although there have been more elaborate ruses.

Hundreds of people were arrested in eastern Bihar state in 2015 for scaling the walls of schools and providing crib sheets and study materials to their relatives during exams.

School authorities also created a furore last May when a student was made to remove her bra in public before an exam to ensure she had not hidden notes inside.

India's information technology ministry last week formally requested that Cambridge Analytica -- the data analysis company at the centre of a Facebook privacy scandal -- provide clarity over its practices by the end of the month.