Alan Henning, from Eccles in Salford, was seized while on an aid mission to Syria last December.
In a statement released via the Foreign Office, his wife Barbara said he had been driving an ambulance stocked with food and water at the time.
Mrs Henning said she had sent messages to IS but had received no response.
“I pray that the people holding Alan respond to my messages and contact me before it is too late”
The militants issued their threat to kill the 47-year-old in a video released last Saturday which showed the killing of another British man, David Haines.
‘Selfless man’
The full statement released from the Henning family read:
“I am Barbara Henning, the wife of Alan Henning.
“Alan was taken prisoner last December and is being held by the Islamic State.
“Alan is a peaceful, selfless man who left his family and his job as a taxi driver in the UK to drive in a convoy all the way to Syria with his Muslim colleagues and friends to help those most in need.
“When he was taken he was driving an ambulance full of food and water to be handed out to anyone in need. His purpose for being there was no more and no less. This was an act of sheer compassion.
“I cannot see how it could assist any state’s cause to allow the world to see a man like Alan dying.
“I have been trying to communicate with the Islamic State and the people holding Alan. I have sent some really important messages but they have not been responded to.
“I pray that the people holding Alan respond to my messages and contact me before it is too late.
“When they hear this message I implore the people of the Islamic State to see it in their hearts to release my husband Alan Henning.”
Mr Henning, nicknamed Gadget by the men he was travelling with, was abducted the day he arrived in Syria to help those affected by the country’s civil war.
In video footage filmed as he stopped en route in Turkey he said “no sacrifice we do is anything compared to what they’re going through every day”.
Mrs Henning’s written appeal comes a day after two high-profile imams in the UK had called for his release in a video posted on YouTube.
Haitham al-Haddad, an imam from the Islamic Sharia Council, said executing the British hostage would be “totally haram (forbidden), impermissible, prohibited according to sharia for a number of reasons”.
And Shakeel Begg, imam at Lewisham Islamic Centre in south London, said he wanted to make it clear he stood “with Alan Henning” and added: “I urge you to understand the nature of this prisoner you are holding – a man of peace.”
The scholars’ appeal to release Mr Henning came after more than 100 British Muslim imams, organisations and individuals expressed their “horror and revulsion” at the “senseless murder” of Mr Haines, and the threats to Mr Henning.
A video showing the killing of Mr Haines was recently released by IS.
His death followed those of two US hostages, both of which were also shown in videos.
BBC.