Relatives of UK peace activist Norman Kember and three colleagues are praying for their release as a deadline set by their captors to kill them approaches.
Norman Kember's kidnappers have claimed he was a spy
A group calling itself Swords of Truth says the men, abducted in Baghdad on 26 November, will be killed on Saturday if all prisoners in Iraq are not freed.
Mr Kember, 74, who was shown in a video blindfolded and shackled, is being held with two Canadians and an American.
Senior Muslim leaders around the world have called for their release.
Mr Kember, American Tom Fox, 54, and Canadians James Loney, 41, and Harmeet Singh Sooden, 32, had travelled to Iraq as a "gesture of solidarity" with Canada-based international peace group Christian Peacemaker Teams (CPT).
The group denies the men are spies.
Dr Daud Abdullah, of the Muslim Council of Britain, told the BBC he was optimistic that appeals for the men's release would be successful.
The human rights specialist travelled to Iraq last year to try to win freedom for British engineer Ken Bigley, who was later murdered.
Dr Abdullah said: "You've heard from Hamas, from Hizbollah, from Islamic Jihad - these are the pre-eminent resistance groups in the regions, and so I am sure that their message will be heard, it will get across.
"What we hope now is that the response will be matched by the passion and by the logic that has been conveyed by these appeals."
But Anas Altikriti, the former president of the Muslim Association of Britain who has also been involved in the negotiations, said talks had brought no breakthroughs.
The BBC's Caroline Hawley in Baghdad said it did not look like it had been possible to establish direct contact with the kidnappers.
She said the Iraqi government had been trying to gather intelligence on them, but had not come up with any information.
Foreign Secretary Jack Straw has called for the kidnappers to make contact with UK officials.
Gary Percesepe from the Baptist Peace Fellowship of North America, of which Mr Kember is a member, said the situation was "certainly serious".
"If you are looking for grounds for optimism there may not be those at present, but there are grounds for hope, because our hope is in God."
Several Sunni clerics called for the release of the four men during Friday prayers at mosques across Iraq.
Ahmed Hassan Taha told worshippers in the predominantly Sunni Azamiyah district of Baghdad: "We ask those who have authority and power to do their best to release the four European people who work in Christian peace organisation.
Terror suspect Abu Qatada has joined calls for the men's release
"In fact, those activists were the first who condemned the war on Iraq."
The head of the world's oldest Islamic movement has also made a personal appeal to the kidnappers.
Mohammed Mahdi Akef, president of Egypt's Muslim Brotherhood - which is officially banned - said the hostages were from a group which worked with Palestinian people "against Israeli aggression" and should be welcomed.
"Kidnapping will only distort the image of Iraq," he said.
Last week a plea by terror suspect Abu Qatada, from Full Sutton jail, near York in northern England, was broadcast in the Middle East.
The cleric, accused by a Spanish judge of being al-Qaeda's ambassador in Europe, called for the hostages to be freed "in line with the principle of mercy of our religion, if there was no compelling religious duty against it".
Mr Kember has been shown in a video wearing a Guantanamo Bay-style orange jumpsuit, saying he was a "friend of Iraq".
Terry Waite, who was taken hostage in Beirut 1987 and held for five years, criticised Mr Kember for going into a "highly polarised" situation in Iraq.
But CND vice-president Bruce Kent defended the visit in a BBC News 24 interview, saying that despite the risks many peacemakers had gone to Iraq in the last two years and returned home safely.
He added: "I think it's much to the honour of the Muslim religion that they have actually rallied in this way to save these innocent people."