Doha said it was reviewing the list, but said it was not reasonable or actionable.
However, Tillerson said the proposals provided a basis for dialogue leading to a solution of the crisis.
Saudi Arabia and its allies require Qatar to cut diplomatic relations with Iran, close the Turkish military base, eliminate Al-Jazeera TV channel and extradite all persons wanted in four countries on charges of terrorism. "Our activities are not against any particular country", Muftuoglu said.
Stop all funding for individuals, groups or organizations designated as terrorists by Saudi Arabia, Egypt, Bahrain, U.A.E., the United States and other countries.
He added: "If you look at the words of Secretary Tillerson, you have to slightly read between the lines, because he has been very careful - all of the countries involved are all close U.S. allies". Tillerson called on all parties to lower their rhetoric and to seek unity in the fight against terrorism.
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Qatar, which had 10 days to respond, is still gauging how to answer. The Ministry of Foreign Affairs said it would give its official response to Kuwait, which has been acting as a mediator between Qatar and its neighbors.
"One day it's Iran, today it's Qatar", he said.
What are the demands that have been issued to Qatar? .
The story raised concerns about the closure of Al Jazeera, citizenship rights and extraditions.
Speaking at the same event, the Iranian foreign minister Zarif said the countries who blamed Iran or Qatar for terrorism were trying to avoid taking responsibility for their own failures in addressing the demands of their own people.
"Some of the elements" in the demands "will be very hard for Qatar to meet", Tillerson said last weekend.
"Demanding that Turkey pull its soldiers is unfortunately also disrespectful toward Turkey", he said.
"I could not have been more pleased with the President's recent trip to Saudi Arabia", Corker wrote to Secretary of State Rex Tillerson in a letter. Trump has announced billions of dollars in arms sales since taking office in January.