The now-banned hardline TLP wants Islamabad to expel the French Ambassador over the issue of blasphemous cartoons.
Foreign ministry spokesman Mohammad Faisal says the Christian woman, who is currently at an undisclosed location for her own safety, is free to leave Pakistan and seek asylum abroad.
Asia Bibi was freed by the Supreme Court in October in a blasphemy case, a verdict the court is reviewing, after religious hardliners seeking her death rioted for days.
Police have arrested Khadim Hussain Rizvi accused of disrupting daily life with rallies across Pakistan following the acquittal of a Christian woman in a blasphemy case.
"I have been told that she is on a plane but nobody knows where she will land," lawyer Saif-ul-Malook says, a week after a top court ordered Bibi's release overturning her conviction that sparked massive protests by hardliners.
Pakistan's information minister Chaudhry Fawad Hussain says his government entered into a deal with the hardline protesters to avoid violence sparked by a top court order that acquitted a Christian woman Asia Bibi of blasphemy charges.
On Wednesday, Pakistan's Supreme Court overturned the conviction of Asia Bibi, a mother of five, and ordered for her to be freed.
Asia Bibi, a Christian woman, was acquitted of blasphemy charges by the Supreme Court on Wednesday sparking violent protests by the country's conservative groups running on third straight day.
Religious groups incensed by acquittal of a Christian woman Asia Bibi for blasphemy vow no let up to protests after Prime Minister Imran Khan promised to confront them.
The trial of Bibi, who is an illiterate mother of five, has become a test case for Pakistan's commitment to protect its minorities, which have born the brunt of blasphemy accusations.
Pakistan's top court has acquitted Asia Bibi of blasphemy charges in a case that led to the deaths of a sitting governor and minister in the past. The decision — viewed as controversial by Pakistani hardliners—has triggered violent protests.
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