But Qatar has not acknowledged that harboring or funding terrorists is the real reason for the diplomatic rift in the first place, which puts the Gulf states - and now Corker - at something of a standoff as the 10-day deadline presented to Qatar for meeting the demands inches closer.
Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman al-Thani speaks to an AFP reporter in Doha, on June 8, 2017.
Nevertheless, he did write that the (P) GCC had failed to "take advantage" of an Arab-Islamic-American summit last month in Saudi Arabia's capital, Riyadh, where Trump and dozens of Arab and Muslim leaders discussed ways of rooting out "terrorism", and "instead chose to devolve into conflict".
In a June 20 briefing, spokesperson Heather Nauert said that Tillerson had held more than 20 calls and meetings with regional and worldwide representatives, which included the foreign ministers of Qatar and Saudi Arabia as well as UAE leaders.
Qatar's foreign minister is set to meet his USA counterpart in Washington, DC, after the U.S. state department voiced confusion over the Saudi-backed embargo of the country.
When asked what will happen if the demands are not fulfilled, al-Jubeir said, "We stay where we are".
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US Urges Qatar, Neighbors To 'Sit Together' To Ease Tension
Tillerson called on all parties to lower their rhetoric and to seek unity in the fight against terrorism . However, Tillerson said the proposals provided a basis for dialogue leading to a solution of the crisis.
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It also questioned the appropriateness of the increase in the Sovereign Grant given it has already gone up 167 percent since 2012. The Queen will receive an 8% increase in her income from public funds after the Crown Estate posted a £24m rise in profits.
Harsh sanctions remain imposed against the gulf country by a Saudi led coalition of states for Qatar's alleged state sponsoring of terror organizations, and a total of 13 demands will need to be met if economic and diplomatic relations are to open again with its Middle Eastern neighbors. They included closing Al Jazeera, shutting down a Turkish military base and cutting off ties with certain political groups. The United States has cautioned that some of the demands would be hard for Qatar to accept, asking the Saudis for a clear list of grievances that are reasonable and actionable.
Tillerson said "there are significant areas which provide a basis for ongoing dialogue leading to resolution".
A USA arms embargo would directly affect recent weapons orders by both Qatar and Saudi Arabia.
He said some of the demands being made of Qatar were negotiable but others clearly challenged its sovereignty. He called for Qatar and the other Arab countries to "sit together" to work through the list.
Bahrain, one of the Saudi allies, has accused Qatar of creating a military escalation in the deepening dispute by letting in more Turkish troops.
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.