On Friday, Tillerson urged Qatar's neighbors to ease their blockade and called for "calm and thoughtful dialogue".
Saudi Arabia also sealed Qatar's only land border, a key passageway for food imports. He says the US asks that there be "no further escalation".
Tillerson, speaking at the State Department, said the USA would help support efforts to mediate the crisis, along with Kuwait - another Gulf country that has stepped up to try to broker a resolution.
A senior UAE official followed on Saturday by calling Qatar "duplicitous", alleging in a series of tweets that its funding of militants had sown chaos and violence throughout the region.
"Diplomacy only way forward. We have to stop the funding of terrorism", said Trump. The port of Dayyer is Iran's closest port to Qatar. "Qatar can not agree with the United States in all the policies, for example Washington considers the Palestinian movement Hamas as a terror group while the Arab countries regard it as a legitimate resistance movement, the diplomat added".
He said Qatar remained committed to a Kuwaiti-led mediation effort, but that he had yet to receive a clear list of demands. "There is a continuous escalation from these countries ... but our strategic options are still diplomacy and dialogue", added Sheikh Mohammed, after holding talks with German Foreign Minister Sigmar Gabriel.
U.S. President Donald Trump delivers remarks during a joint news conference with Romanian President Klaus Iohannis in the Rose Garden at the White House in Washington, U.S. June 9, 2017. On Saturday, he told Bahrain's foreign minister that the dispute should be resolved by the end of the holy month of Ramadan.
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Trump cited that, as his outside lawyer has as well, as evidence that there was no collusion or obstruction in his administration. Trump's presidency has been all about playing to his base so far, and his base, in this instance, is returning the favour.
Ashcroft's firm includes an array of former senior government officials including Sullivan, a former USA attorney in MA appointed by Bush to lead the Bureau of Alcohol, Tobacco, Firearms, and Explosives (ATF).
Arab nations, including Saudi Arabia, the United Arab Emirates, Egypt and Bahrain have accused Qatar of supporting terrorism and destabilizing the region because of its ties to their Shiite rival, Iran, and its support for groups like the Muslim Brotherhood and Hamas.
New Delhi is closely following the emerging situation in the Gulf region in the wake of the recent decision by Saudi Arabia and some other countries, the Ministry of External Affairs said in a statement.
USA president Donald Trump is ramping up pressure on Qatar to stop what he calls a "high level" of financial support of terrorism.
Qatar will pay the Ashcroft Law Firm $2.5 million (2 million pounds) for a 90-day period as the country seeks to confirm its efforts to fight global terrorism and comply with financial regulations including U.S. Treasury rules, according to a Foreign Agents Registration Act, or FARA, filing on Friday with the Justice Department.
Trump said "Nations came together and spoke to me about confronting Qatar over its behavior".