The decision to not publish the report has caused an outcry and intensified allegations that the government is delaying publishing the report, which was ready six months ago, in order to save diplomatic ties with Saudi Arabia - a country largely expected to be named in the paper as financing extremists in Britain.
They stated again that the embargo against Qatar would continue until Doha commits to comprehensively implement the demands.
French Foreign Minister Jean-Yves Le Drian will fly to Gulf states at the week-end to help end ongoing diplomatic row with Qatar, the foreign ministry said Wednesday in a statement.
The shutdown of the network is on the list of demands from the quartet.
Qatar has so far denied any wrongdoing.
It also claims the boycott has led to human rights violations, and yesterday one group said abuses were one effect of the crisis.
On Tuesday, Tillerson signed an agreement with Al Thani aimed at combating "terrorism financing", a deal Saudi Arabia and its allies branded as being "insufficient".
After Doha, Tillerson is set to tour other gulf capitals as part of United States mediation in the ongoing Gulf crisis.
US Senator, Bob Corker, has made headlines with his comments calling Saudi Arabia's crown prince, Mohammed bin Salman's participation in the Gulf blockade of Qatar a "rookie mistake". Physical exercise for women has been a controversial topic for many in the country, with some religious authorities deeming it immoral, regardless of the approval from the Saudi Shura Council for female sports back in 2014.
The United States and its Western allies have vast economic and political interests in the Gulf, which pumps one fifth of the world's oil supplies.
Corker said he was "really disappointed to see what Saudi Arabia did after having a great summit and bringing everybody together", referring to May's Riyadh conference that saw leaders of the GCC and other Arab states meet US President Donald Trump.
Qatar is home to the US's largest miilitary base in the region. Rival Bahrain houses the US Navy Fifth Fleet. Calling the demands, which were presented to Qatar on June 22, unworkable, Qatar has publicly claimed the list was deliberately created to be impossible for it to meet.