Shahid Orakzai filed the petition in the Lahore High Court, in which he argued that the three PML-N leaders had already been disqualified by the apex court.
He contended that the Sharif brothers and Rafiq were convicted in a case related to an attack on the Supreme Court in 1997 but they did not mention this in their nomination papers for the May 11 polls.
Lahore High Court Chief Justice Umer Ata Bandial yesterday adjourned the case till June 11.
The Chief Justice asked Orakzai why he did not challenge the qualification of the respondents and orders of the tribunals before a full bench that heard election-related matters before the general election.
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Orakzai, a former close associate of Nawaz Sharif, said a constitutional petition could be filed at any time.
PML-N activists had attacked the Supreme Court during Sharif's last tenure as premier.
Sharif is set to become premier for a record third term after the PML-N won the May 11 general election.