On Wednesday, the top court acquitted Aasia Bibi - a Christian woman accused of blasphemy in 2010 and sentenced to death - and set aside an earlier judgment passed by a lower court.
Following the verdict, the patron-in-chief of the Islamist Tehreek-e-Labaik political party is reported to have stated that the chief justice and those who ordered Aasia's release "deserve death".
In a statement issued today, HRCP has said: While there is every reason to be relieved that Aasia Bibi has been acquitted after eight years of incarceration in the perpetual shadow of a death sentence, that Pakistan should have come this close to executing a woman for "blasphemy" is a sobering thought.
Asia's family and her lawyer say she never insulted the prophet.
The party has launched street protests blocking roads in major cities to condemn the ruling, which was welcomed by human rights advocates.
BBC News reporter Secunder Kermani, on the ground in Islamabad on Wednesday, wrote, "Asia Bibi's lawyer, closely flanked by a policeman, told me he was "happy" with the verdict, but also afraid for his and his client's safety".
The court has set no dates to take up the petition, but Bibi's release could be further delayed by the process.
Meanwhile, opposition lawmakers in parliament called on Thursday for reforming the judicial system and Pakistan's controversial blasphemy law - so that innocents like Bibi wouldn't spent years languishing in jail.
Approximately 40 people are believed to be on death row or serving a life sentence in Pakistan for blasphemy, according to a 2018 report by the United States Commission on International Religious Freedom.
Ms Asia Bibi's case drew the attention of global rights groups and swiftly became the most high-profile in the country. "Will they let me out, really?" she said.
Pakistan Army on Friday warned hundreds of radical Islamists hardliners not to test their "patience" and asked them to end the standoff peacefully to avoid the use of force as the mass protests against the acquittal of a Christian woman for blasphemy entered its third day.
Protesters chanted "hang the blasphemer" and "hang the judges" as they marched through the capital in the absence of a heavy security presence.
Chief Justice Saqib Nisarm, who read out the verdict, said October 31 that Bibi is free to leave the prison in Sheikhupura, Pakistan. In many cities of Punjiab there are demonstrations and roadblocks.
Pakistani Christian woman Asia Bibi at a prison in Sheikhupura near Lahore, Pakistan, on November 20, 2010.
"I don't see any derogatory remarks vis-a-vis the holy Koran as per the FIR", added Chief Justice Nisar, referring to the initial complaint filed in the case. The farm workers who pressed charges denied they quarrelled with her, saying her outbursts against Islam were unprovoked. She was accused of making offensive comments about the Prophet Muhammad in the ensuing argument, in response to claims she should convert to Islam. But they said prosecutors had failed to prove that Bibi violated the law.
Such protests will distract Prime Minister Imran Khan's government, which is attempting to deal with an economy in crisis owing to dwindling finances.
Critics of the blasphemy law have said it is used to settle personal scores or to attack minority communities.
"Clearly she will need asylum in a western country where she can live out the remainder of her days in peace", Wilson Chowdhry, chairman of the British Pakistani Christians Association, told CBN News.