Theresa May has said she will not be drawn into sharing specific details of the UK Government's involvement in Asia Bibi's bid for asylum.
The Prime Minister was pressed on the matter by MP for Gillingham and Rainham, Rehman Chishti, during Prime Minister's Questions on Wednesday.
Mr Chishti told the Prime Minister that if the UK asked a third country to take in the Christian Pakistani woman, 'that would mean shifting our moral responsibility to another country and that can't be right'.
Bibi recently gained her freedom after years in prison on blasphemy charges but remains in hiding due to the continued threat to her life from Muslim hardliners.
Her lawyer fled the country immediately after her acquittal at the end of October and her two daughters have reportedly been sent out of the country for their safety, while her husband lives with her in hiding.
The family has appealed to the UK and other Western countries to grant asylum but so far, no official offer has been made.
Mr Chishti asked Mrs May whether Foreign Secretary Jeremy Hunt's review into Christian persecution would change the Government's position on Bibi's bid for asylum.
The MP, who resigned as Vice Chairman of the Conservative Party over the Government's treatment of Bibi, said the UK should make an offer of asylum 'so she can choose which safe destination she wants to go to'.
Mrs May responded to his question in the Commons on Wednesday by saying that the safety of Bibi was the UK Government's 'primary concern'.
'Our primary concern is for the safety and wellbeing of Asia Bibi and her family and obviously the UK High Commissioner in Islamabad is keeping me and the Government up to date with developments,' she said.
'We have been in contact with international partners about our shared desire to see a swift and positive resolution in this case, and a number of countries are in discussion about a possible alternative destination for Asia Bibi once the legal process is complete,' she said.
'I'm not going to comment on the details of that because we do not want to compromise Asia Bibi's long-term safety.'
She added that Pakistan's Foreign Minister had given assurances that Bibi would remain under government protection until the legal process had concluded and that Prime Minister Imran Khan supported the Supreme Court and had promised to uphold the rule of law.
She concluded: 'What matters is ensuring that we are providing for the safety and wellbeing of Asia Bibi and her family.'
It is not the first time Mrs May has faced questions in Parliament about Britain's handling of Bibi's case.
Soon after her release from prison and as pressure mounted on Britain to take her in, the Prime Minister denied accusations that she had blocked an offer of asylum out of concern that it would stoke tensions with Muslims at home.
She said at the time: 'We could approach this in two ways. We could go out there and say something, just to show that the UK is doing that, or we could ask what is right for Asia Bibi.
'We are working with others in the international community and with the Pakistani Government to ensure that our prime aim—the safety and security of Asia Bibi and her family—is provided for.'