Peers have strongly criticised the Government over its handling of Asia Bibi's plea for asylum.
The Christian mother-of-five is being persecuted by hardliners in Pakistan after being freed from death row last month.
The UK is among several Western countries that her family has sought asylum from but so far, no concrete offer has been made and she remains in Pakistan.
On Wednesday, Prime Minister Theresa May denied reports that she had refused to offer Bibi asylum on the grounds that it would stir up tensions among British Muslims.
Responding to a question from Zac Goldsmith, she said the Conservative MP 'should not necessarily believe everything he reads in the papers'.
'The position that the Government take is very clear: our prime concern must be the safety and security of Asia Bibi and her family, and we want to see a swift resolution of the situation,' she said.
'Obviously, there is a primary function for the courts and Government in Pakistan. The Prime Minister, Imran Khan, has publicly supported the Supreme Court and has promised to uphold the rule of law, while providing continued protection for Asia Bibi.
'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.'
But on Friday, several peers including Lord Alton of Liverpool and Baroness Cox wrote in The Times that a failure to offer her asylum would be a 'serious betrayal'.
'Britain's position indicates a serious betrayal of our time-honoured commitment to offer asylum to those in need,' they said.
'It also undermines our belief in justice, human rights, the rule of law and religious freedom, and risks us falling foul of, and succumbing to, blackmail.'
The Government has previously come under fire from former Foreign Secretary Boris Johnson, who said Bibi had an 'overwhelming claim for compassion from the British government'.
'I am well aware, as a former Foreign Secretary, of the constant threat to our overseas missions, but we cannot allow the threat of violence to deter us from doing the right thing,' he said in a letter to Home Secretary Sajid Javid.
The failure to offer asylum also prompted the resignation of Rehman Chishti as Conservative Party Vice Chairman and the Prime Minister's trade envoy to Pakistan.
'What I found shocking, is that the British Government is failing to put into practice the core values that our country stands for; religious freedom, justice, morally doing the right thing, and that when we see injustice where an individual's life is in clear danger and they have been persecuted for their faith, we do all that we can to help them,' he wrote in his resignation letter.
'The Government should not wait to see if another country offers sanctuary, we should have had the conviction to lead on this matter and offer sanctuary ourselves straight away.'
