Also, the initial legislation related to Aadhaar during the UPA regime was a "bald" one, Mr 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".
"...the UPA government had two clear schools of thought. One which was not enthused by Aadhaar at all and therefore raised issues... relating to national security. And the other (school of thought) which was pushing it. As a result, (it) was a very bald legislation," said Mr Jaitley.
On Congress' stance on the legislation, the finance minister remarked, "Where do you stand now literally depends upon where you sit in the House."
Mr Jaitley was speaking at the launch of a book 'Aadhaar: A Biometric History of India's 12-Digit Revolution' written by Shankkar Aiyar in Delhi.
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.