Tillerson flew into Saudi Arabia where he met King Salman and Crown Prince Mohammed bin Salman, whose country leads a four-state alliance that has cut ties with Qatar over accusations it supports extremism.
The United States, a longtime ally of Sunni-ruled Saudi Arabia, has given mixed signals about its policy on the Gulf crisis.
While President Donald Trump welcomed the Arab states' decision to sever air and land links to their gas-rich neighbour, the State Department has taken a more neutral position and Tillerson is seeking to broker a diplomatic solution.
In a setback to his efforts, the four Arab states yesterday dismissed a counter-terrorism deal signed between Qatar and the United States that day as "insufficient".
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But today Tillerson underscored the shared mutual interests between the United States and Saudi Arabia notably in the areas of "security, stability... And economic prosperity".
Speaking after meeting with the Saudi crown prince, the king's son and a highly influential figure in regional politics, Tillerson stressed the two countries shared a "strong partnership".
The United States and its Western allies have vast economic and political interests in the Gulf, which pumps one fifth of the world's oil supplies.
While Saudi Arabia is a key US ally, Qatar is home to the US military's largest air base in the region, Al-Udeid. Rival Bahrain houses the US Navy Fifth Fleet.
Yesterday, after a stop in regional mediator Kuwait, Tillerson travelled to Doha where he described Qatar as being "reasonable" in its dispute with the four states.
The deal meant Qatar was "the first to respond" to Trump's call at a summit in Riyadh in May "to stop the funding of terrorism", Tillerson said, suggesting such deals could be signed with the other Arab states as a step toward ending the crisis. But yesterday's initiative was dismissed as "insufficient" by the Saudi-led bloc.
Commitments made by Qatari authorities "cannot be trusted," said a joint statement published by Saudi state news agency SPA.
Iran, Saudi Arabia's main arch-rival, has offered to export food to Qatar and today announced it was boosting ties with the Gulf state of Oman.
Oman has maintained ties with Qatar and joined the Kuwaiti and US-led crisis talks this week.
Saudi Arabia, the UAE, Egypt and Bahrain on June 5 announced sanctions, effective immediately, against Qatar over accusations Doha supported Islamist extremism and was too close to Iran.
They severed all diplomatic ties, suspended transport links with Doha and ordered all Qataris to return home within 14 days.
UN rights chief Zeid Ra'ad Al Hussein on June 30 said the demand to close Al-Jazeera represented "an unacceptable attack on the right to freedom of expression and opinion," prompting a harsh response from the United Arab Emirates.
In a letter to the rights chief, UAE state minister for foreign affairs Anwar Gargash accused Al-Jazeera of anti- Semitism and inciting viewers to discrimination and violence.
The letter lists the broadcasting of "sermons by the spiritual leader of the Muslim Brotherhood, Yusuf al-Qaradawi, in which he praised Hitler, described the Holocaust as 'divine punishment'" and the regular airing of the speeches of slain Al-Qaeda chief Osama bin Laden and others as examples of hatred.
French Foreign Minister Jean-Yves Le Drian will visit the Gulf this weekend, with stops in Qatar, Saudi Arabia, the UAE and Kuwait.