Saudi Arabia, Bahrain, the United Arab Emirates and Egypt cut ties with Qatar in June, accusing it of supporting terrorism and cozying up to Iran. Doha denies the charge.
Tillerson made an unsuccessful attempt to resolve the dispute during a trip to the region in July.
US President Donald Trump, after initially appearing to support the effort to isolate Qatar, has called for mediation and recently predicted a rapid end to the crisis.
"I do not have a lot of expectations for it being resolved anytime soon," he said in an interview with financial news agency Bloomberg.
"There seems to be a real unwillingness on the part of some of the parties to want to engage."
Aside from the Gulf dispute, Iran, the conflict in Yemen and counter-terrorism also are on the agenda in the Gulf, the State Department said.
While in Riyadh, Tillerson will also take part in the first meeting of a Saudi-Iraqi coordination council, a sign of warming relations between the Sunni-ruled kingdom and Baghdad as the Saudis seek to counter Tehran's influence in Iraq.
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