The proposal was made by China and India at the United Nations.
The government's move comes a month after the Parliament passed an amendment to the Unlawful Activities Prevention Amendment (UAPA) Bill, 1967. The new law empowers the government to designate an individual as a "terrorist".
People of India heaved a collective sigh of relief when China finally withdrew its veto and permitted the listing of the architect of Pulwama attack as an international terrorist.
Rahul Gandhi, while addressing a press conference at the party headquarters, said Modi insulted the Army by saying UPA's surgical strikes were video games.
Pakistan-based Azhar is also banned from selling or purchasing arms and ammunition.
A UNSC designation will subject Azhar to an assets freeze, travel ban and an arms embargo.
A known fugitive, Azhar, who formed the JeM in 2000, was branded the brain behind various suicide strikes in India.
China put a technical hold in March on a fresh proposal to impose a ban on the head of Pakistan-based JeM which claimed responsibility for the deadly Pulwama terror attack.
China on Wednesday dismissed reports that the US, UK and France have served it an ultimatum until April 23.
Chinese Foreign Ministry spokesman Geng Shuang told a media briefing that Washington move only complicates the issue.