They want Doha to close the al-Jazeera TV channel, restrict diplomatic ties with Iran, halt the construction of a Turkish military base in the country, and sever contacts with extremist organisations.
But his Secretary of State, Rex Tillerson, acknowledged on Sunday that some of the demands issued by its neighbours would "be very hard to meet" and called for "dialogue leading to resolution".
The closure of the broadcaster is said to be one of 13 wide-ranging demands placed on Doha by Saudi Arabia and its allies as the price for lifting their nearly three-week-long "blockade" of Qatar.
As a measure to lower the terrorist threat, Qatar is expected to stop naturalization of citizens from Saudi Arabia, the UAE, Bahrein and Egypt, as well as to give out all the criminals, those countries are searching for.
"This list of demands confirms what Qatar has said from the beginning-the illegal blockade has nothing to do with combating terrorism, it is about limiting Qatar's sovereignty, and outsourcing our foreign policy", said Sheikh Saif bin Ahmed Al-Thani, head of Qatar's government communications office.
Coffey says "it's a list of impossible demands for Qatar".
Speaking at a news conference on Saturday, Gargash called for guarantees from Western countries to help resolve the row.
The list of demands on Qatar, which was leaked Thursday, included requirements that Qatar shutter its popular Al Jazeera news channel - which has been critical of neighboring monarchies - and scale back its relations with Iran.
The ultimatum doesn't specify what action the Saudi-led group might take against Qatar if it fails to agree to the demands by the deadline.
It also urged universities and educational institutions in the UAE, Saudi Arabia and Bahrain to put aside political differences and take into account the rights of Qatari students and do not put obstacles to their right to education.
Accusing Qatar of supporting terrorism, Saudi Arabia, the United Arab Emirates, Egypt and Bahrain cut ties with Doha on June 5.
"Relations between Iran and Qatar have always been developing and strong", he added.
The U.S. also has continued to offer arms to Qatar, including a $12 billion deal for as many as 36 F-15 jets that was completed this month amid the Gulf crisis. The Trump administration is hoping to close business and investment deals with the Saudis worth more than $350 billion, while the biggest US military base in the region, Al Udeid Air Base, is in Qatar.