"A productive next step would be for each of the countries to sit together and continue this conversation", said Tillerson, confirming that Qatar has begun the review of the demands issued by the Saudi-Emirati-led bloc of countries amid the worst crisis in the Gulf in decades.
Turkish President Recep Tayyip Erdogan slammed a series of sweeping demands several Arab countries have made against their Gulf neighbor Qatar, including that the emirate shut down the Turkish military base on its territory. A lowering of rhetoric would also help ease the tension.
On June 5, Saudi Arabia, Egypt, the UAE and Bahrain cut off diplomatic ties and imposed a blockade on Qatar, accusing it of supporting terrorism and undermining regional security.
Mr Tillerson said Qatar was assessing the demands and stressed there were "significant areas which provide a basis for ongoing dialogue leading to resolution". "Their role should be to put pressure on Qatar", said Gargash. "Each country involved has something to contribute to that effort", he said.
Last week, before the anti-Qatar demands became public, State Department spokeswoman Heather Nauert was unusually blunt in criticizing the group of nations isolating Qatar and effectively dared them to come up with a list of Qatari misdeeds. USA will continue to support mediation efforts of Emir of Kuwait. The anti-Qatar countries claimed Qatar's royal family has been funding terrorism, but their list of demands suggests they are pressuring Qatar as a way of trying to isolate Iran and suppress media in the region that have been critical of governments throughout the Middle East.More news: Istanbul Pride: Turkish riot police fire rubber bullets at LGBT marchers
The blockade of Qatar is "unacceptable" and Tehran's policy is to strengthen ties with Doha, Iran's state-run Islamic Republic News Agency cited President Hassan Rouhani as saying on Sunday.
"NHRC noted that Qatar's acceptance of these demands and conditions would subject the country to worldwide accountability and violate its obligations on human rights conventions".
The diplomatic gulf crisis broke out after the decision by Saudi Arabia, Bahrain, the United Arab Emirates, Egypt, Yemen and Libya, and the Maldives in the early hours of Monday, June 4 to sever their ties with Qatar over its alleged "support of terrorism".
"We view cooperation with the Qatari government as continuous cooperation and believe that there are very good opportunities to further deepen relations between the two countries and these opportunities must be exploited", Rouhani said, according to statement on his website. "Re-evaluating the base agreement with Qatar is not on our agenda".