The Prime Minister has dismissed reports that she blocked an offer of asylum to a Pakistani Christian woman being hounded for her faith.
Asia Bibi has been forced into hiding after being acquitted of blasphemy charges at the end of October.
She spent the last eight years in solitary confinement in a Pakistani prison before being released three weeks ago. But her release sparked angry protests across Pakistan and calls for her death from Muslim hardliners.
Her family has made appeals for asylum to several Western countries, including the UK, US and Canada, but a formal offer has not yet been forthcoming.
The Daily Mail reported over the weekend that Theresa May had refused an appeal by Home Secretary Sajid Javid to offer the family in the UK.
According to the newspaper, the request was turned down by the Prime Minister over fears that it could stir up tensions among British Muslims and compromise the safety of British officials in Islamabad.
During Prime Minister's Questions on Wednesday, Conservative MP Zac Goldsmith asked May if there was any truth to the reports and whether the UK was planning to offer the family sanctuary.
In her reply, May said the minister 'should not necessarily believe everything he reads in the papers' as she insisted that Britain was working for the 'safety and security' of Bibi and her family.
'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.'
Politicians have joined Christian campaigners in calling on the UK to offer asylum to Bibi. John Pontifex, of Aid to the Church in Need, told the Guardian that the family are fearing for their safety as tensions continue to run high over her acquittal.
'Mullahs had been reported in their neighborhood going from house to house showing photos of family members on their phones, trying to hunt them down,' he said.
Earlier this month, Rehman Chishti resigned as Conservative Party Vice Chairman and the Prime Minister's trade envoy to Pakistan, citing Britain's failure to offer asylum to Bibi as one of the reasons.
'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.'
