Lawyers for Mohammed Asghar told campaigners at Reprieve that they have serious concerns about his mental wellbeing.
He appeared "pale, dehydrated, shaking and barely lucid", and suffering from severe delusions during a recent visit by lawyers, it is claimed, prompting fears his condition has seriously deteriorated.
Mr Asghar was arrested in 2010 in Rawalpindi, near Pakistan's capital, Islamabad, for claiming to be the Prophet Mohammed.
His family says he suffers from mental illness and was treated for paranoid schizophrenia in Edinburgh before returning to Pakistan in 2010.
He was convicted last week but his family is appealing for him to be released from custody in order to receive medical help.
Reprieve said lawyers for Mr Asghar finally gained access to their client today.
As a result, they were able to get the necessary documents signed so that he can file his appeal against the sentence.
But they told the charity they have concerns for his mental health and say that, despite his diagnosis of paranoid schizophrenia, prison medical staff remain unaware of his serious psychiatric illness and are not giving him the appropriate medication.
During their visit, it was "clear" he was in very poor health and they have stressed it is crucial he receives the expert medical treatment he urgently needs.
Maya Foa, director of Reprieve's death penalty team, said: "We are extremely worried about Mr Asghar's mental health, which appears to have seriously deteriorated.
"We are also extremely concerned by the reports that he is not being given the correct medication for his illness, putting him in a perilous position.
"We hope that the authorities in Pakistan and the UK will take all necessary steps to ensure that he gets the expert treatment he needs without delay."
The blasphemy complaint was brought against Mr Asghar by a tenant with whom he was having a dispute.
Yesterday, Mr Asghar's family appealed to the UK Government to do everything it can to make sure he is safe.
In a statement released through Reprieve, his relatives said: "We, his family, want him released by the Pakistani government so he can be treated appropriately for his medical condition.
"As a result of a property dispute with one of his tenants, my father was jailed pending a trial.
"The dates kept being moved forward so that by the time the trial concluded he had already been in horrific jail conditions, sharing a cell with several other men for three years.
"Throughout this time he had minimum access to medication that might have helped his mental illness for three years.
"We are really upset and concerned that they will never release him and that he will die in jail."
A petition on change.org, addressed to Prime Minister David Cameron and Scotland First Minister Alex Salmond, is calling for Mr Asghar's release.
The Foreign and Commonwealth Office (FCO) said it has continuously made representations to the Pakistan government on behalf of Mr Asghar and would continue to do so.
The Scottish Government said it was in touch with the Foreign Office about the case.