Thousands of supporters of outlawed Tehreek-e-Labbaik Pakistan are marching towards Islamabad with a series of demands including the release of their imprisoned leader.
The now-banned hardline TLP wants Islamabad to expel the French Ambassador over the issue of blasphemous cartoons.
The ban, instated until 1100 GMT on YouTube, Facebook, WhatsApp, Twitter and Telegram, comes as government tries to stem days of anti-French protests by supporters of now-banned far-right Tehreek-e-Labbaik Pakistan.
Security forces block off capital Islamabad to contain thousands of protesters gathered outside the city to protest against republication of caricatures in France insulting Prophet Muhammad.
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.
The country's new chief justice says the request to review her acquittal was rejected on merit. The Christian woman sentenced to death in 2010 in what swiftly became Pakistan's most infamous blasphemy case.
Street power is often used as a tool to pressure Pakistani governments to the extent that the state often loses the ability to protect its citizens.
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.
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