Mentally ill Mohammad Asghar, 70, was convicted in January for claiming to be a prophet of Islam, an act considered sacrilegious in Pakistan, which is 97 per cent Muslim. The verdict prompted Cameron to say he was "deeply concerned" about Asghar's fate.
Asghar was hospitalised last month after being shot and wounded in jail.
Daughter Jasmine Rana today arrived at Cameron's Downing Street office with a petition signed by 70,000 people calling on the prime minster to secure her father's return.
"His life remains at risk for as long as he is held in Pakistan. I have come to London today to ask the prime minister to intervene to bring dad back home," said the woman, who lives in Scotland's main city of Edinburgh.
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Many in Pakistan are devout Muslims, and extremist currents are present in the country. Even unproven allegations of slights against Islam can provoke violent responses.
Asghar, a British-Pakistani with dual nationality who has lived in Britain for 40 years, was sentenced by a court in Rawalpindi, near the capital Islamabad, for writing letters claiming to be a prophet of Islam.
Kate Higham, an investigator at anti-death penalty campaigner group Reprieve, said Cameron should treat the case as an "absolute priority".