A Saudi coalition of states has placed 13 demands on Qatar to lift their blockade, including the closure of Al Jazeera and what it states are publications and websites "directly or indirectly supported by Qatar".
The list from Saudi Arabia, the UAE, Bahrain and Egypt also calls for Qatar to cut all ties with Iran, pay compensation to the petitioning states for "victims and losses" due to Qatari foreign policy and a 10-year "mechanism" to ensure Qatar sticks to the deal.
The media organisations the petition claims are "supported" by Qatar include Arabi21, al-Araby al-Jadeed, Sharq, and the London-based Middle East Eye.
Qatar has 10 days to accept the demands, it said.
David Hearst, Middle East Eye's editor-in-chief, said his organisation was not funded by Qatar - or any other state or group - and was here to stay.
"Middle East Eye is independent of any government or movement and is not funded by Qatar," he said.
"Maybe the fate of Al Jazeera will depend on talks between the government of Qatar and its neighbours. But Middle East Eye is here to stay.
"MEE covers the area without fear or favour, and we have carried reports critical of the Qatari authorities, for instance how workers from the subcontinent are treated on building projects for the 2022 World Cup."
On Thursday, the UAE's foreign minister Anwar Gargash accused Al Jazeera of being a "news broadcast for the Muslim Brotherhood".
"It is a mouthpiece for extremism. It has whitewashed personalities that have become symbols for terrorism."
Hearst said these claims, and the petition's demands for other media to close, were designed to strangle independent views.
"Obviously this is an attack on anyone in the Middle East who dares to offer an independent opinion," he said.
"Mr Gargash is frightened of something we in Britain call a free press. The only media he knows is one whose editorial line he can dictate and whose journalists he can buy. I have news for him. That world is disappearing."