– ‘Profound crisis’ –
The list of demands has not been officially confirmed.
Gargash alleged Qatar had leaked them in “an attempt to abort the mediation in a childish act that we have grown accustomed to from our brother”.
“It would be wiser that (Qatar) deal seriously with the demands and concerns of the neighbours or a divorce will take place,” he wrote on Twitter.
The demands confirm that “the crisis is profound,” Gargash added.
Qatar faces a choice of either stability and prosperity, or isolation, he said.
“Perhaps the solution is in parting ways.”
Qatar is a member of the Gulf Cooperation Council with Bahrain, Kuwait, Oman, Saudi Arabia and the UAE.
On June 5, Saudi Arabia and the UAE led a severing of all links with Qatar for allegedly supporting groups, including some backed by Iran, “that aim to destabilise the region”.
Other allies, including Egypt and Bahrain, followed.
Saudi Arabia regularly accuses Iran, its regional rival, of interference throughout the Middle East.
– US ‘mystified’ –
As well as cutting diplomatic ties, Qatar’s neighbours closed their air space to Qatari carriers and blocked the emirate’s only land border, vital for its food imports.
The list of 13 demands circulating on social media also says Qatar must cut ties to groups including the Muslim Brotherhood, the Islamic State organisation, Al-Qaeda and Lebanon’s Iran-backed Hezbollah movement.
Qatar is also required to hand over opposition figures wanted by its three neighbours and Egypt.
In addition to Al-Jazeera, it must shut online information sites that it supports, according to the reported demands.
“The brother (Qatar) must realise that the solution for its crisis lies not in Tehran or Beirut or Ankara or Western capitals or in media outlets, but in regaining the trust of its neighbours,” Gargash said.
“It is not possible to accept that the brother continues as the Trojan horse” in the Gulf or as a funder and “platform for an extremist agenda”, he added.
Earlier this week, a foreign diplomat told AFP the crisis had reached a “stalemate” and “won’t end soon”.
Tillerson said on Wednesday that Washington had been pushing for a clear list of grievances that are “reasonable and actionable”.
“Our role has been to encourage the parties to get their issues on the table, clearly articulated, so that those issues can be addressed and some resolution process can get underway to bring this to a conclusion,” he said.
His spokeswoman Heather Nauert said Tuesday the United States was “mystified” that Saudi Arabia and its Gulf allies had failed to present details justifying their embargo on Qatar.
US President Donald Trump, however, has made statements siding with Saudi Arabia in the crisis.