Their father Martin Weekes said no one outside the Qatar Government had seen any facts about the fire or the investigation report.
"It's distressing and hurtful to all the families who lost their loved ones killed in the Villaggio Mall to see and hear stories like this stating that the mall fire was an act of terrorism aimed at Qatar.
"However, in the absence of the Qatari authorities releasing the investigation report into the fire or providing specific detail into the cause and the subsequent recommendations on improving public safety to Villaggio Mall rumours will always circulate to fill the void of real information," he said.
Prime Minister John Key said yesterday he had seen media reports but no evidence to indicate the fire was not accidental.
"Obviously we take these sort of reports seriously, and so I've asked my officials to go away and drill down, have a look and see if there's any merit to these reports," Mr Key said.
Mr Weekes, along with the families of the others killed in the fire, have never been briefed on the investigation.
Saudi-owned Al Arabiya was not independent and the only "facts" on how the fire started were reported from a press release on the Qatar Government's official news agency, he said.
"This also states we the families have been briefed on the fire and the investigation which we know is untrue, therefore in the absence of the report who knows the real facts," he said.
Mr Weekes urged authorities to continue their investigation and include the families whose testimony and firsthand accounts from the scene could be vital to their findings.
Leon Goldsmith, a Middle East expert who spent seven years studying the area, told TV3 last night Al Arabiya was "relatively professional but you'd have to read their stories with a certain grain of salt or at least be careful to cross-reference".
Its direct competitor, Al Jazeera, is not reporting the story.
TV3 quoted an Al Jazeera journalist as saying there was "a void of information from the Government about the [mall] fire, so rumour and speculation abound".