They discussed the possibility that British soldiers from Afghanistan use it to call home without being detected by the Taleban, or allowing Libyan rebels to use it to avoid detection by Muammar Gaddafi's forces, the Financial Times said.
Speaking in Tripoli, Fox said the Dubai meeting came about by chance while he was on a stopover from Afghanistan.
"Actually the defence industry representatives asked for it when they happened to be sitting at a nearby table in a restaurant, so it's not that unusual," Fox told the BBC.
"But with these questions, they're all reasonable questions for people to ask and I don't mind that and that's what you get in a democratic society."
The claims overshadowed Fox's first visit to Libya on Friday and Saturday, during which he announced £500,000 (NZ$1,009,000) new funding for the National Transitional Council's fight against arms proliferation.
In London, Cameron's spokesman initially said he would wait for the outcome of the MoD inquiry, led by the ministry's top civil servant.
But as the row gathered pace, Downing Street said Cameron had asked the head of Britain's civil service to look at the initial findings of the MoD inquiry and ensure they were on his desk on Monday.
"The prime minister has asked the cabinet secretary to examine the initial findings of the Ministry of Defence permanent secretary's review, and report his conclusions to him on Monday," a spokeswoman said.
She could not say whether that early report would be made public.
Saturday's allegations come after Fox admitted this week that he met Werritty on an official visit to Sri Lanka in July, and the revelation that Werritty visited Fox 14 times in 16 months at the MoD in London.
Fox has denied suggestions that his friendship has threatened national security, and an MoD spokesman said allegations of wrongdoing were "baseless".
According to The Independent, the Financial Times and The Guardian, Werritty set up a meeting with Fox and members of the Porton Group, including chief executive Harvey Boulter, while Fox was in Dubai on official business in June.
Citing Boulter, the newspapers said much of the meeting involved a discussion of Cellcrypt, a technology developed by one of the group's companies which they were interested in selling to the MoD.
The Times reported that Werritty had printed up business cards with a parliamentary seal saying he was Fox's adviser.
Jim Murphy, defence spokesman for Britain's opposition Labour party, called for Fox to make a full statement to parliament on the issue.
"An inquiry is important but so too are direct answers," he said. "There are accusations mounting. It is time for the avoidance to stop and for the answers to start."
-AAP
