Retired general Anthony Zinni told US news network CBS he had quit "because of the unwillingness of the regional leaders to agree to a viable mediation effort that we offered to conduct".
His resignation was confirmed by State Department spokesperson Robert Palladino.
"General Zinni's mission was to help introduce the concept of the Middle East Strategic Alliance and start a conversation with leaders in the region," Palladino told AFP.
"This is happening and well underway thanks to his efforts. The administration... will carry the mission forward," Palladino said in Amman where he accompanied Pompeo on the first leg of his regional tour.
The Middle East Strategic Alliance (MESA) is a NATO-style security pact which Zinni had been asked to introduce to regional leaders.
Zinni, according to CBS, felt there was no need for his involvement in MESA since other members of the US administration of President Donald Trump were already involved in implementing it.
Pompeo launches Mideast tour vowing no Islamic State return
Zinni was appointed by former secretary of state Rex Tillerson in August 2017, two months after the dispute between Qatar and the Saudi-led bloc erupted.
On June 5 of that year, Saudi Arabia, Bahrain, the United Arab Emirates and Egypt cut ties with key US ally Qatar, accusing it of supporting "terrorist groups" and advocating improved ties with their rival Iran.
Qatar, home to a huge US airbase, has denied the claims.
Sustaining a regional coalition to counter Iran, is a major focus of Pompeo's tour of eight Arab capitals in as many days.
The trip will include stops in the six countries that form the Gulf Cooperation Council (GCC) -- Saudi Arabia, Qatar, the United Arab Emirates, Kuwait, Bahrain and Oman -- as well as Egypt and possibly Iraq.
State Department officials have said Pompeo hopes his trip will fortify the GCC which has been weakened by the Gulf diplomatic crisis, and organise a summit of its leaders in the United States later this year.
Zinni once commanded US forces in the Middle East. After the military he served as special envoy to Israel and the Palestinian Authority.
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