Pakistani officials said their request was aimed at tackling fake accounts used to spread hateful messages.
They met Facebook representatives last week, a month after a man received a death sentence in Pakistan for allegedly posting blasphemous message on Facebook.
Pakistan said WhatsApp already has the feature.
Pakistan's Interior Minister Chaudhry Nisar had previously threatened to permanently block social media platforms not cooperating with his anti-blasphemy crackdown. In 2012, Pakistan had briefly blocked Twitter after some users reportedly encouraged others to draw Prophet Muhammad, considered blasphemous under Islam.
Pakistan's Interior Minister Chaudhry Nisar met Facebook's public policy chief Joel Kaplan to discuss the recent blasphemy case.
A Pakistani official said Facebook had promised to "look into the government's concerns on a priority basis."
Facebook said it had a "constructive meeting" where it raised concerns over the case.
It, however, said it would continue authenticating accounts through email addresses, not mobile numbers.
"Facebook met with Pakistan officials to express the company's deep commitment to protecting the rights of the people who use its service, and to enabling people to express themselves freely and safely," said a spokeswoman representing the social media firm.
Love World news?
Subscribe to stay updated.