CBS News quoted Zinni as saying he stepped down from his Trump administration assignment after realising he could not resolve the Gulf dispute.
Qatar remains cut off from Saudi Arabia, the United Arab Emirates, Bahrain and Egypt a year after its Arab neighbours enforced a blockade.
The Qatari government upgrades the status of some foreign residents.
Qatar filed a wide-ranging legal complaint at the World Trade Organization to challenge a trade boycott by Saudi Arabia, Bahrain and the UAE.
Led by Saudi Arabia, several states in the Middle East and Africa have severed ties with Qatar since June 5, accusing the gas-rich Gulf state of supporting terrorism and Iran. Qatar denies the allegations.
The memorandum of understanding was signed on the second leg of US Secretary of State Rex Tillerson's visit to the region in a bid to break the deadlock between Qatar and a Saudi-led block of four nations.
The birth of Al Jazeera sparked a massive disruption to the status quo in the Gulf and Arab world. The evolution of the network, and the ensuing media wars, gives valuable historical insight into the friction between Qatar and its Gulf rivals.
Led by Saudi Arabia, several Arab states have severed diplomatic ties with Qatar since Monday, accusing it of supporting terrorism and for its ties with Iran. Follow are the latest developments in the rift.
The diplomatic rift between Arab Gulf countries who cut diplomatic ties with Qatar has already impacted the country's economy and air travel.
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