The bench, headed by Sardar Muhammad Shamim Khan, issued notice on a civil miscellaneous application, filed by the father of Zainab, Muhammad Amin Ansari.
Earlier, petitioner's counsel argued that the anti-terrorism court concerned had issued black warrants for execution of the condemned prisoner, Imran Ali, in Zainab murder case, after dismissal of his appeals and mercy petition.
He said that the court had directed the jail authorities for hanging Imran Ali on Oct 17.
He submitted that under Section 22 of the Anti-Terrorism Act 1997, the government was empowered to hang a convict publicly, complaining that the government was not complying with the law available on the subject.
He asked the court to order the government to ensure that the convict was hanged publicly to satisfy the requirement of deterrence in society.
The bench, after hearing initial arguments, issued notices to home secretary Punjab for Oct 16 and sought reply.
The high court, on a similar petition by Amin earlier, had referred the matter to the government.
Imran Ali was sentenced to death in February 2018 on charges of kidnapping, raping and killing minor Zainab in January 2018 within the jurisdiction of the A-division police station, Kasur.