Sheikh Mohammed bin Abdulrahman Al-Thaniaddressed his neighbouring states on Monday asking them to life the blockade that Qatar has had to face.
Kuwait, which mediated to end the crisis but was not a part of, handed Qatar the list of demands from Egypt, Saudi Arabia, Bahrain, and the UAE.
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 countries besieging Qatar will present a list of demands in the next few days through Kuwait, Turkish presidential spokesman Ibrahim Kalin said in statements carried by Anatolia Agency.
Gargash called on Qatar to stop harbouring individuals who are sanctioned regionally and internationally for terrorism, as he put it.
Qatar has yet to publicly respond to the demands.
The demands aimed at ending the worst Gulf Arab crisis in years appear created to quash a two decade-old foreign policy in which Qatar has punched well above its weight, striding the stage as a peace broker, often in conflicts in Muslim lands.
The base is a guarantor of the security of Qatar and the Gulf, and demands for its closure showed interference in our ties with Doha, he added.
All means of funding to groups designated as terrorists by Saudi Arabia, the UAE, Bahrain, Egypt and the United States, among other countries, must be cut off.
The total number of Turkish military personnel in Qatar is now 113, according to Turkish media.
Qatar, the world's top exporter of liquefied natural gas, admits that it supports Islamist groups, but denies backing or financing terrorism.
Besides, Qatar must shut down diplomatic posts in Iran, expel any members of Iran's Revolutionary Guard, and only conduct trade and commerce with Iran that complies with United States sanctions. Saudi Arabia and other Sunni-led nations have accused Qatar of inappropriately close ties to Iran, a Shiite-led country and Saudi Arabia's regional foe.
In addition to Al-Jazeera, it must shut online information sites that it supports, according to the reported demands.
Sever all ties to "terrorist organizations", specifically the Muslim Brotherhood, the Islamic State group, al-Qaida, and Lebanon's Hezbollah. Most recently, The Associated Press reports, U.S. Secretary of State Rex Tillerson had been frustrated at perceived delays in formulating the list of demands - but the wire service notes the U.S. official also warned the demands should be "reasonable and actionable".
Turkey has sent more than 100 cargo planes carrying supplies to Qatar, but is now also shipping food over to meet the country's additional needs.
Not to fund any other TV stations, including Al Jazeera, Arabi21 or Middle East Eye.