They also suspended all land, air, and sea traffic with Qatar, ejected its diplomats, and ordered Qatari citizens to leave their countries.
Qatar faces isolation by fellow Arab countries after Saudi Arabia, Bahrain, United Arab Emirates (UAE) and Egypt severed ties with Doha on Monday, accusing it of supporting Islamist militants and their adversary Iran.
While Tillerson and others have called for an easing of tensions, Trump said on Friday that Qatar had "historically been a funder of terrorism at a very high level".
Senegal has said it would recall its ambassador in Qatar and expressed its "active solidarity".
"Qatar is confident that the review and analysis will confirm that Qatar has significant measures in place to prevent and detect efforts to launder funds and/or to use its financial systems to finance terrorist organizations", he said.
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Kuwait's foreign minister said on Sunday that Qatar was ready to listen to the concerns of other countries in the Gulf, state news agency KUNA reported, and that his country would continue its efforts to patch a rift within the Gulf.More news: Kickboxer Murthel Groenhart KO's Opponent, Gets Attacked By Fans in Ring
Among the six Gulf Cooperation Council (GCC) states, Kuwait and Oman did not join the anti-Qatar blockade and the Kuwaiti leadership has been communicating with all parties of the crisis to reach a solution.
Affected families were urged to call hotlines set up by authorities in the three countries to get assistance, the statements added without giving details.
Qatar was importing 80 percent of its food requirements from bigger Gulf Arab neighbors before they cut ties with the nation of 2.5 million people last week.
Ethiopia's foreign ministry said in a statement it did not support any kind of negative media reports that incite instability in countries.
Iran also announced it had sent tons of vegetables to Qatar, which has seen food imports threatened.
Tillerson urged Saudi Arabia and other Gulf states Friday to "no further escalate" the crisis and ease their blockade of Qatar, which he said was causing unintended humanitarian consequences and affecting the US -led fight against Islamic State.
Eritrea declined a request by Saudi Arabia and the UAE to cut diplomatic ties with Qatar, according to a statement issued by Eritrean foreign ministry.