But on Monday, Qatar's Foreign Affairs Minister Sheikh Mohammed bin Abdulrahman Al-Thani said the country would only begin negotiations to end the crisis after measures taken against the country were lifted.
The demands include cutting back Qatar's diplomatic ties to Iran.
Acting as a mediator, Kuwait has presented Qatar a long-awaited list of demands from Saudi Arabia, Bahrain, the United Arab Emirates and Egypt - four Arab nations that cut ties with Qatar in early June.
Turkey will not close its military base in Qatar, Turkish Defense Minister said on Friday in reply to a demand by four Arab countries to end boycott against Doha.
Saudi Arabia, the United Arab Emirates, Bahrain and Egypt severed diplomatic ties with Qatar on June 5 after accusing it of funding extremism and destabilizing the Middle East.
The list of 13 demands circulating on social media also says Qatar must cut ties to extremists including the Muslim Brotherhood, Islamic State group, Al-Qaeda and Lebanon's Iran-backed Hezbollah movement.
Those four countries have now given Qatar 10 days to comply with all of the demands.
"There are no IRGC (Iranian Revolutionary Guard Corps) elements in Qatar and the agreement with Turkey is a long-standing diplomatic agreement so we can not ask them to leave".
- Stop interfering in the four countries' affairs.
If Qatar agrees to comply, the list asserts that it will be audited once a month for the first year, and then once per quarter in the second year after it takes effect.More news: Teen who fell from Six Flags ride remains hospitalized
- Cut ties to terrorist organizations.
Cutting ties to Iran would prove incredibly hard.
Turkey's military support for Qatar has been matched by stepped up commercial links.
"The leak (of the demands by Qatar) is an attempt to abort the mediation in a childish act that we have grown accustomed to from our brother", Gargash wrote on Twitter.
The demands include an insistence that Qatar - long considered by its neighbours to be a maverick - align itself "militarily, politically, socially, economically" with other Gulf and Arab states.
Kuwait, which is mediating the dispute, handed the list to the Qatari government, they said.
"Shut down Al Jazeera channels and affiliated channels", said point six of the document written in Arabic, the title of which translates as Joint Requirements for Qatar.
"It does seem as if this is Saudi Arabia bullying its tiny neighbor and ganging up on it", analyst Greg Barton of Australia's Deakin University told Turkey's state-funded TRT World.
"The base in Qatar is both a Turkish base and one that will preserve the security of Qatar and the region", he said. They have also insisted on imposing a monitoring mechanism which would report regularly on Qatar's compliance with the demands.