Also, the initial legislation related to Aadhaar during the UPA regime was a "bald" one, Jaitley said.
The finance minister recalled that Nandan Nilekani gave a "forceful and persuasive" presentation to Prime Minister Narendra Modi, who decided to go ahead with it, soon after the NDA government came to power.
However, he said, when the Act was reworked by the present government, "one thing which was clear that the privacy provisions were required".
He further said that when the present government decided to go ahead with Aadhaar, the UPA, now in Opposition, almost made it clear that they were opposed to this idea.
On Congress' stance on the legislation, Jaitley remarked, "Where do you stand now literally depends upon where you sit in the House."
Jaitley was speaking at the launch of a book 'Aadhaar: A Biometric History of India's 12-Digit Revolution' written by Shankkar Aiyar here.