The move is an attempt to legalise the status of a large number of children who were born legally but whose parentage is unknown, National Database and Registration Authority Chairman Malik Tarek said.
NADRA plans to issue identity cards to thousands of children of unknown parentage, a majority of whom were dropped by their parents at welfare centres, Tarek told The Nation daily.
A large number of such children arrived at welfare centres after losing their parents in the 2005 earthquake and last year's devastating floods, he said.
NADRA was at a loss about filling the registration forms for such children as it is mandatory to mention the name of the father and mother, he added.
"When it came to the knowledge of President Zardari, he voluntarily offered his name to be used in the father's name box for such people," Tarek said.
"I want you to make a strategy to make thousands of children with unknown parentage responsible citizens of the state.
"NADRA can mention my name as father of all such children to issue them identity cards," Tarek quoted Zardari as saying.
In order to deal with the sensitive and complex issue of children of unknown parentage, NADRA approached different schools of Islamic thought in countries like Saudi Arabia and Iran and some suggested that "Adam and Hawa" should be named as the father and mother of such children.
"We took a fatwa from leading Islamic institutions and scholars of Saudi Arabia and Iran to deal with the issue," Tarek said.
NADRA also consulted social workers like Abdus Sattar Edhi, chief of the Edhi Foundation.
Welfare centres where the children are living will be named as their guardian, Tarek said.
Pakistan has no law on the rights of illegitimate children, including their financial entitlement or inheritance, legal experts said.
They suggested the government should organise a conference to discuss how to register illegitimate children as they too have a right to good education and jobs.