On Friday, US President Donald Trump also turned up the heat on Qatar, warning it to stop "funding terrorism" while his state department urged Arab states to ease their blockade on the country.
Since then, Saudi Arabia, United Arab Emirates, Egypt, Bahrain and Egypt have severed diplomatic ties and transport links with Qatar.
Gulf Arab nations, with the exception of Kuwait and Oman, acted because of Qatar's longtime support for militant Islamist groups such as Hamas and the Muslim Brotherhood, as well as the nation's ties with regional rival Iran.
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.
On Tuesday, Trump seemed to endorse the Gulf states' action in a series of tweets.
But Mr Trump said that he, Mr Tillerson and military leaders decided during his trip to Saudi Arabia last month that a public rebuke was needed.
Trump added that "all reference was pointing to Qatar".
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"The blockage is hindering United States military action in the region, and the campaign against ISIS", Tillerson said, using an acronym for the extremist group. He warned that the Persian Gulf crisis is hindering USA efforts to fight the Islamic State group.
President Donald Trump offered Wednesday to personally broker a resolution to the Persian Gulf's escalating diplomatic crisis, as both he and Qatar looked past his pointed suggestion only a day earlier that the tiny gas-rich nation enables terrorism.
Qatar on Friday rejected allegations of supporting individuals and groups blacklisted as "terrorists" by a bloc of Arab neighbours that has imposed an economic blockade on it amid a major diplomatic fallout.
The statement said that Trump emphasised the importance of all countries in the region working together to prevent the financing of terrorist organisations and stop the promotion of extremist ideology. "Have no choice", Trump said.
The president has followed the lead of Saudi Arabia and the UAE, publically backing them in their media war with Qatar. He asks the Gulf nations to "de-escalate the situation" and ease the blockade against Qatar.
The president said Qatar must end its support for extremism, along with "all other nations".
The base is the nerve-center for USA air operations for Iraq, Syria, Afghanistan and other Middle East nations. "We will continue to give all our support to Qatar", Recep Tayyip Erdogan said at an iftar (fast-breaking meal) with members of his Justice and Development (AK) Party in Istanbul.
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