Mirza due to be hanged on April 1 was convicted in 1999 for killing the then Karachi Electric Supply Corporation chief Shahid Hamid, his driver Ashraf Brohi and guard Khan Akbar in 1997.
His execution was delayed last week after a video surfaced in which he alleged that top leaders of the Muttahida Qaumi Movement (MQM) had ordered the killings.
MQM Chief Altaf Hussain rejected the allegation and said he will file a case against Mirza.
But the government has now asked President Mamnoon Hussain to postpone his execution further, by another 30 days.
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Under the Constitution, the head of state can stay the execution if there are some legal issues involved.
It is believed that government wants to use Mirza's statement against the MQM which is not happy with the ongoing security operation in Karachi.
An MQM delegation today met Sharif and expressed its reservation over the operation.
Civil society and lawyers have assailed the government for allowing the recording of video message of a death row prisoner which is against the law, saying his statement is of no value in a court of law.
Mirza has been kept in Machh jail, Balochistan since April, 2014. The jail is notorious for lodging mostly hardened criminals.