The Christian mother-of-five was acquitted of blasphemy in Pakistan last week and has been released from prison.
Reports indicate she was flown from a detention facility in southern Punjab to Islamabad amid tight security.
Her acquittal prompted thousands of people to join protests in several major cities, demanding that she be publicly executed.
The Citizengo petition reads: "We at CitizenGO wish to help take Asia Bibi and her family out of the country and give them a better life. However, they are now prohibited from leaving Pakistan, and her court case might be reviewed.
"That is why we are asking the Pakistani Prime Minister, Imran Khan, to intercede as soon as possible so that this Christian woman and her family can leave, and that the necessary security measures will be taken to keep them alive.
"We also ask United Nations Secretary General António Guterres, US President Donald Trump, and the High Representative of the European Union for Foreign Affairs and Security Policy, Federica Mogherini, to pressure Khan with all available diplomatic tools in order to achieve complete freedom for Asia Bibi and her family."
Citizengo and the British Pakistani Christian Association (BPA) will hold a one-hour silent vigil outside the Pakistan High Commission on Monday at 3pm in support of Asia Bibi.
Wilson Chowdhry, chairman of the BPA said: "Asia Bibi has been reunited with family during a tearful reunion. Their joy is however tempered with fear as they await a decision from the petition to the Supreme Court challenging her acquittal.
"I don't believe any Supreme Court judge could deny the authority of that decision when there is no right of appeal to any person or entity, and should be summarily dismissed.
"However, the fact Asia Bibi's case is fraught with controversy and political machinations will no doubt play a factor.
"So we must urge people to pray that the chosen judges be bold in their desire to uphold the rule of law over the socio-political factors that could cause a travesty of justice."
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