Mohammad Asghar, from Edinburgh, was sentenced to death earlier this year after being convicted of blasphemy in 2010.
Last month the 70-year old, who has been diagnosed with paranoid schizophrenia, was shot and wounded by a guard at the Rawalpindi prison where he was being held.
He has been in intensive care in hospital since the shooting, where campaigners saying he remains gravely ill.
Amnesty International Scotland has launched a new campaign, calling for Mr Asghar’s sentence to be quashed and for him to be freed.
They hope members of the public will get behind their letter-writing appeal to help put pressure on the authorities in Pakistan to take action in this case.
Amnesty launched the drive on World Day against the Death Penalty.
Siobhan Reardon, Amnesty International’s programme director in Scotland, said: “It is inconceivable that Mohammad Asghar was attacked by a prison guard - the very person who should be providing protection.
“This is clear evidence that those accused of blasphemy in Pakistan are never safe from vigilante violence. He was sentenced to death despite being diagnosed with a serious mental disability.
“Blasphemy carries a potential death sentence in Pakistan - in direct contravention of the country’s international human rights commitments.”
Mr Asghar was jailed in January after writing a series of letters claiming to be the Prophet Mohammed.
“As the recent shooting incident shows, Mohammad is in mortal danger every day he remains on death row and we are urging the UK government to step up efforts to get him out of prison and into a place of safety,” Ms Reardon said.
“Mr Asghar should never have been sentenced to death for writing letters - he should be released immediately and his sentence quashed.”
The appeal - at www.amnesty.org.uk/pakistan - comes as Amnesty warns that numerous countries around the world have also sentenced people to death despite evidence of them having mental and intellectual disabilities.
The charity argues that is a clear violation of international standards on the death penalty.
It says it has documented cases of people suffering mental and intellectual disabilities facing execution or being executed in countries including Japan, Pakistan and the United States.
Ms Reardon added: “The international standards on mental and intellectual disability are important safeguards for vulnerable people. They are not designed to excuse horrendous crimes - but to set clear guidelines for the nature of the penalty that can be imposed.
“We oppose the death penalty in all circumstances - it is the ultimate cruel, inhuman and degrading punishment. But in those countries that still execute, international standards, including those prohibiting the use of capital punishment on certain vulnerable groups, must be respected and implemented, pending full abolition.”