The fresh appeal came after Britain's Foreign Office officials told relatives of Alan McMenemy and Alec MacLachlan that the two security guards were "very likely" to be dead, the BBC reported. The families then issued a statement noting they were "deeply upset and troubled," by the reports.
"We ask those holding our men for compassion when so many are working hard for reconciliation in Iraq," the statement said. "And we continue to pray for the safe return of our men."
The fate of the hostages has been murky ever since Shiite militants disguised as Iraqi policemen abducted the five Britons outside Iraq's Finance Ministry in May 2007. Since then, the men have only been seen in videotapes made by their captors.
The fate of Peter Moore - the technology consultant they were guarding - is unknown, while the bodies of two other British hostages, Jason Swindlehurst, 38, and Jason Creswell, 39, were returned to England in June. The men, who worked for the Canadian security firm GardaWorld, suffered multiple gunshot wounds.
Moore's grandmother, Edna Moore, 84, said the family could only wait.
"We can only hope," she said. "God help the other families... There's not much we can do, we feel so helpless."
The Foreign Office would not officially confirm the BBC report but said every effort is being made to secure the release of the hostages and that families were being kept informed.
Hopes for the men had risen after the release in June of Laith al-Khazali, a Shiite militant who had been held in U.S. custody. The kidnappers want nine militiamen released, including al-Khazali's brother, Qais al-Khazali, in exchange for the British hostages.
Laith al-Khazali, a Shiite militant allegedly backed by Iran, was released as part of national reconciliation efforts between the Iraqi government and groups that renounce violence. He and his brother were accused of organizing a daring attack on a local government headquarters in Karbala that killed the five U.S. soldiers on Jan. 20, 2007.
If the hostages are found to have been harmed, it could impact delicate negotiations between Iraqi Prime Minister Nouri al-Maliki's government and al-Khazali's Asaib Ahl al-Haq group - or League of the Righteous - which was aimed at getting the group to disarm and play a role in politics once the hostages had all been freed.