The Army of Islam spokesman came to prominence after threatening to kill Johnston in June if the UK failed to release Abu Qatada, an Islamic cleric who is being held in a British prison.
The group has also since threatened to release what it said were damaging documents about Hamas if Qatada was not freed.
In June, the group posted a video on the internet showing Johnston strapped with an apparent explosives belt.
Johnston reportedly said in the video that his captors threatened to blow him up if force was used to try to free him.
"The situation now is very serious as you can see I have been dressed in what is an explosive belt which the kidnappers say will be detonated if there was any attempt to storm this area," Johnston said.
Johnston was seized at gunpoint as he drove home from work in Gaza City on March 12.
In the first video released after his abduction Johnston said his captors were treating him well and spoke of the suffering that Gazans had endured because of sanctions imposed on the Hamas-led Palestinian government.
He also criticised the British military presence in Afghanistan and Iraq, saying: "In all this, you can see the British government is endlessly working to occupy Muslim lands against the will of the people in those places."