He warned that the Persian Gulf crisis is hindering US efforts to fight the Islamic State group.
Trump has aligned himself closely with Saudi Arabia and an allied bloc of Arab countries since taking office.
The confrontation in the region intensified on Friday as Arab states tightened their squeeze on Qatar by putting dozens of figures with links to the country on terrorism blacklists, while Qatar's ally Turkey rushed to its side with plans to send troops. The Turkish President has promised to continue supporting Qatar after Saudi Arabia, UAE, Bahrain and Egypt severed ties with tiny but resource-rich emirate, accusing Doha of funding terrorist organizations, RT reports. Saudi Arabia, however, is locked in a regional power struggle with Iran. "Qatar remains critical for coalition air operations in the fight against ISIS and around the region".
"We ask that there be no further escalation by the parties in the region", Tillerson said Friday.
Qatar's foreign minister fired back that there was "no clarity" in such accusations, speaking in an interview with RT Arabic in Moscow after emerging from talks with Russian Foreign Minister Sergei Lavrov.
UK Conservatives need to deliver an "open" Brexit - Scotland leader
In Scotland an entirely different election campaign ran in parallel to that taking place in the rest of the UK. But writing on Twitter this morning, the Scottish Tory leader dismissed the newspaper claim as "b****cks".
Russian Federation yesterday urged dialogue between the parties, as Qatar's foreign minister arrived in Moscow seeking support from overseas in the dispute.
Trump too had offered possible mediation earlier in the week.
Increasing the pressure on Friday, Qatar's neighbours put 12 organisations and 59 people on a terror sanctions list and described them as being associated with Qatar.
Qatar saw an alliance with the Brotherhood and its movement as a hedge against dominance by Saudi Arabia; Saudi Arabia and the United Arab Emirates saw the same forces as a threat to the stability of their governments and the region.
In separate statements Saturday, they lauded Trump for his supportive stance. Several Qatari charities were also named, and Qatar denied that they were involved in financing terrorism. "I decided ...the time had come to call on Qatar to end its funding", Trump said, adding that he helped plan the Qatar action with Arab leaders after a recent summit in Riyadh, Saudi Arabia.
Tillerson says the US will support efforts to mediate the crisis along with Kuwait.
SNP could deny 'arrogant' Tories a Westminster majority - Nicola Sturgeon
Pressed on the date, she added: "Look, you're putting arbitrary dates in my ... you know, I believe Scotland will be independent, I've always believed that".
The biggest concentration of United States military personnel in the Middle East is at Qatar's Al Udeid Air Base. Kuwait's ruler, meanwhile, is making an effort to help mediate.
Rights group Amnesty International says thousands of Gulf residents are now caught up in the dispute.
Qatar's neighbors have also given its citizens 14 days to leave and instructed their own nationals to return. They also warned that anyone who expresses support for Qatar online faces imprisonment and hefty fines. "The format of dialogue among the states of Persian Gulf is the most appropriate format for such dialogue".
"These drastic measures are already having a brutal effect, splitting children from parents and husbands from wives".
Dialogue is the best way to tackle the political rift in the Arab world over Qatar, two top diplomats said Saturday in Moscow. He also risks losing his job.
Apple CEO Tim Cook to address 2017 graduates at MIT
Don't get caught in the trivial aspects of life. "Don't listen to the trolls, and for God's sake don't become one", Cook added. He said Francis told him, "Never has humanity had such power over itself, yet nothing ensures that it will be used wisely".
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