Qatar, a major United States ally, has been in the spotlight since four major Arab powers, including Saudi Arabia and Egypt, severed their ties with the country and accused it of supporting terrorism and working secretly with Iran, the arch-foe of the Saudis.
Trump on Friday accused Qatar of being a "high-level" sponsor of terrorism, potentially hindering the US Department of State's efforts to ease heightening tensions and a blockade of the Gulf nation by Arab states and others.
On June 7 and 8, Saudi Arabia, the United Arab Emirates and Bahrain announced that any speech sympathetic to Qatar or critical of their governments' policy towards Qatar would be considered an offense, punished in some cases by prison terms.
Turkish Foreign Minister Mevlut Cavusoglu on Wednesday urged dialogue to end a crisis that has left Ankara's ally Qatar diplomatically and economically isolated after key Gulf neighbours cut ties, following talks with the Qatari emir in Doha.More news: Supreme Court rules for Missouri church in playground case
The ministry said Qatar had been an "impartial diplomatic mediator" in resolving border disputes between Eritrea and Djibouti. "The blockade is hindering United States military actions in the region and the campaign against ISIS", Tillerson said, without providing details.
Turkey also is eager to maintain workable relations with Iran, Saudi Arabia's foe with whom Doha's critics say Qatar maintained excessively close ties. Qatar acknowledges its links to these groups, but denies that it supports terrorism.
The US ambassador to Qatar said Tuesday she is resigning her post in Doha amid the worst diplomatic crisis involving Washington's Persian Gulf allies in years. Countries have pledged $6 billion to help Syria, but so far only 22 per cent of that has been funded, said Marcy Vigoda of the U.N. Office for the Coordination of Humanitarian Affairs.
Saudi Press Agency (SPA) said King Salman and Sharif discussed the "latest regional developments" in addition to bilateral relations.