Ken Bigley's brother claims he has new information he is alive in Iraq but says Tony Blair's silence could be the "kiss of death" for the hostage.
There has been no word on Ken Bigley for several days
Paul Bigley thought the family's pleas were getting through; his "gut feeling" was that his brother would come home.
He said on the BBC: "Ken's had enough, we've had enough. Just let the man come home to his mum, please."
Earlier, he told a Labour conference fringe meeting: "Just send a bloody fax pleading for my brother's life."
He urged the meeting to press Tony Blair to ask George W Bush to release women prisoners in Iraq, as demanded by the kidnappers.
At the start of his speech to the Labour party conference on Monday, Chancellor Gordon Brown expressed his sympathies.
"The thoughts of everyone at this conference today are with Ken Bigley and every member of his brave family," he told delegates.
A team of British Muslims had spent the weekend meeting the Iraqi president and religious leaders from the Sunni, Shia and Christian communities to try and secure Mr Bigley's release.
Dr Daud Abdullah and Dr Musharraf Hussain - who are returning to Britain on Monday - said they were encouraged by promises all was being done to try and open a dialogue with the captors.
In a message to the militants they said Ken Bigley was a victim just like the people of Fallujah, the eastern city in Iraq which has endured a weekend of US raids, and should not be punished.
The leader of Liverpool's Muslim community, Mohammad Akbar Ali, visited the area in which the Bigleys live at the weekend and said co-operation between different religions was vital.
"It is a humanitarian cause. It is important to show to the world that Muslims and Christians can
work together, particularly in times such as these of emergency and distress.
"Of course we have differences but those are insignificant - we are all human beings, something we should not ever forget," he said.
Paul Bigley has criticised Mr Blair for "only going through the diplomatic instruction book" in his efforts to free his brother.
Speaking via a telephone link to a Labour Against the War meeting in Brighton on Sunday, Mr Bigley said: "I have received information this evening that Ken is alive. Ladies and gentlemen, delegates, we can keep him alive.
"Please could you on my behalf, on behalf of my brother somehow ask Mr Blair to pick up the bloody phone and call President Bush and ask him to take off the blockade on these women prisoners?"
He urged Mr Blair to send a message to the Middle East media begging for his brother to be spared, as the Irish government had done many times already.
Mr Bigley said he believed there was work being done behind the scenes but British officials did not understand how to work in the Middle East.
Attacking what he branded an "immoral war", he urged Mr Blair to withdraw British troops.
On Monday he told BBC Radio 4's Today programme he knew a "damn sight" more about how to operate in the Middle East than Mr Blair.
Ken Bigley, a civil engineer from Liverpool, was captured at gunpoint in Baghdad on 16 September with two American colleagues, who have both since been murdered.
He is being held by the hardline Tawhid and Jihad group, led by Abu Musab al-Zarqawi, one of the world's most wanted men.
They have demanded the release of women prisoners.