Though Kuwait is officially mediating the dispute, Tillerson has been actively involved making phone calls to the leaders of each country in an effort to break the impasse. Tillerson has already said that parts of the demands "will be very hard for Qatar to meet".
Doha denies the accusations it supports terrorism and described as "unjustified" the moves to isolate it.
Anwar Gargash, the UAE's foreign minister, said on Saturday that Qatar "cannot be a Trojan horse" with regard to regional security. The immediate result, however, has been a ban of the use of land, air and water routes for the movement of people and goods involving the territory of the three GCC countries.
The meeting may also help clarify seemingly contradictory positions between Tillerson and Trump on Qatar's crisis.
A report by Kuwait's Al-Seyassah daily says that Kuwaiti officials have continued their efforts to provide an atmosphere of agreement to settle the crisis in the Persian Gulf.
The countries have presented a 13-point ultimatum to Qatar but Doha has rejected their demands as unrealistic.
"The goal of the deployment of the Turkish Armed Forces in Qatar is to contribute to the security of the region as well as to provide Qatar with support in military training", the Turkish Ministry of Foreign Affairs said in a June 25 statement.
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Qatar has said it won't negotiate until the sanctions are lifted.
"We approve and appreciate the attitude of Qatar against the list of 13 demands ..."
The story raised concerns about the closure of Al Jazeera, citizenship rights and extraditions. "In this context NHRC urged the state of Qatar not to accept those demands", the article said.
Meshal Hamad Al-Thani, Qatar's ambassador to the United States, tweeted that the list was meant to "punish Qatar for its independence". Other demands call on Doha to publicly denounce relations with Islamist groups, end the suspected financing of terrorism and hand over persons designated as terrorists by Saudi Arabia, the United Arab Emirates, Bahrain and Egypt.
Qatar-flagged and -owned vessels remain banned from ports in the UAE and Saudi Arabia, and Qatar's airline is banned from routing flights through Saudi airspace.
Recently, QIIB chief executive Abdulbasit Ahmad al-Shaibei said Qatar has contingency plan for the worst case scenario and it immediately activated the contingency plan following the blockade.
A handout picture provided by the office of Iranian President Hassan Rouhani shows him speaking at a conference in the capital Tehran.