The shadowy group who have held BBC correspondent Alan Johnston for the last three months have threatened to kill him in a video broadcast by the Al-Jazeera satellite TV channel.
A spokesman for The Army of Islam, identified as Abu Khattab, told Al-Jazeera that there was no deal to release Mr Johnston, and "if the situation gets more complicated concerning us and our group, then we will ingrate ourselves to Allah by slaying this journalist".
The authenticity of the video could not be independently confirmed.
Earlier, a Hamas spokesman in Gaza said there had been no new developments in the case, despite reports that Johnston would be released soon.
After taking control of the Gaza Strip last week, Hamas officials said they had made contact with Mr Johnston's kidnappers and would work to win his release.
Negotiations were said to be taking place between Hamas and Mr Johnston's captors through a mediator. Hamas spokesman Islam Shahwan said: "All I can say is that Alan will be free very soon."
Mr Johnston, 45, from Argyll, has been held since March when he was snatched by the group, which are believed to have some links to Hamas.
A message purporting to be from his captors has demanded the release of Islamic prisoners, including a cleric being held in Britain.
His disappearance is the longest of any Western journalist abducted in Gaza and has sparked numerous protests and solidarity marches in London and the Palestinian territories.
Palestinian officials have said they know where to find Mr Johnston, but have held back on raiding the hideout at Britain's request, for fear of harming him.
