Tillerson will shuttle between Kuwait, Qatar, Saudi Arabia from Monday to Thursday in what is the first serious intervention by Washington in the Gulf crisis.
The dispute has seen a Saudi-led alliance impose sanctions on Doha over its alleged ties to both Islamist extremist groups and Shiite-dominated Iran.
As they met in Egypt last week, Saudi Arabia and its allies said they planned to tighten sanctions against the gas-rich emirate, after Qatar refused to comply with a list of demands.
"Right now, after Egypt, we're months away from what we think would be an actual resolution and that's very discouraging," RC Hammond told reporters.
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On June 5, Saudi Arabia, the United Arab Emirates, Bahrain and Egypt abruptly severed diplomatic ties with Qatar, suspending transport links with Doha and ordering all Qataris to repatriate within 14 days.
The four nations later issued a list of 13 demands to be met to lift the sanctions, including that Qatar shut down broadcaster Al-Jazeera, close a Turkish military base and downgrade diplomatic ties with Iran.
Tillerson, the former chief executive of energy giant Exxon Mobil, arrives in the Gulf after a stop in Istanbul, where he discussed the Syria war to a failed 2016 coup in Turkey.
Analysts say Tillerson's success in the Gulf may be contingent on his ability to maneuver regional skepticism over conflicting stances from Washington on the crisis.
US President Donald Trump initially supported longtime US ally Saudi Arabia, but his stance was later contradicted when the US Department of State took a more neutral position.
"If Tillerson can convincingly frame his mission as delivering a deal for the United States that is all about defeating terrorism... Then he may have some chance," said Partrick, who focuses on Gulf politics.
But despite strong mediation efforts by Kuwait and others, governments across the region say they may remain deadlocked for the foreseeable future.
"No diplomatic effort or... Mediation will succeed without Doha being rational, mature and realistic," UAE state minister for foreign affairs Anwar Gargash tweeted last week.
UK National Security Advisor Mark Sidwell is scheduled to attend part of the meeting between Tillerson and Kuwait's Foreign Minister Sheikh Sabah Khaled Al-Sabah.
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