Auckland Council is asking the Government to review the exemption for the Waiheke ferries, potentially bringing the struggling service under the supervision of Auckland Transport.
The call follows reports of violence and tension on Waiheke ferries caused by reduced winter sailings, which was seeing commuters left behind.
At the moment, Fullers does not come under Auckland Transport's oversight, under a deal struck with the former Transport Minister Steven Joyce.
Auckland Mayor Phil Goff made the announcement this morning alongside Auckland Transport boss Lester Levy.
Goff said too many ferry sailings were being delayed, cancelled or sold out - and too many passengers were being left behind.
"Whether or not it's unsubsidised or private, it is an integral part of our public transport system across Auckland.
"We need to know we do have the level of reliability people on Waiheke deserve and respect."
Goff said the Waiheke to city service was a critical commuter service.
"Whether you're living on Waiheke, you don't have another way of getting home.
"If you're travelling to Devonport and the ferry's cancelled, you can hop on a bus over the Harbour Bridge. You can't do that on Waiheke."
If Transport Minister Phil Twyford removed the exemption, it would bring the Waiheke ferries under the same conditions as other public transport operators in Auckland.
Last month the Herald reported frustrated Waiheke commuters were resorting to violence against ferry staff amid escalating tensions caused by reduced winter sailings to the island.
Passengers desperate not to be left on the dock were reportedly lashing out at crew, including pushing and shoving Fullers workers, and shouting abuse if the ferry was full.
In one instance queuing customers even "held the gangway hostage" by refusing to move aside while there were still spare seats on the departing ferry - left empty when there aren't enough staff to meet health and safety ratios - delaying the boat and leaving staff shaken.
The National Government brought in the current public transport model to encourage competition in the sector. But former National Transport Minister Steven Joyce exempted Fullers' services from the model, against Auckland Transport's wishes.
That exemption meant Auckland Transport couldn't see into the business.
Explore pulled its services in 2016, leaving Fullers as the sole ferry provider for Waiheke. Fullers halved its winter sailings this season.
Fullers chief executive Mike Horne said he was concerned about the level of frustration of some of its customers.
"There's certainly a level of angst that's building with our staff, and my priority is making sure that I'm looking after those customers but certainly my staff and wellbeing of the crew," he earlier said.
Horne insisted the issue of missing boats was a rare occurrence, and overloading happened usually only during peak weekend sailings.
Horne said having to wait was the thing that wound up the commuters to the point where they were quite angry.
He denied it was a problem on weekdays, and said since the winter timetable came into operation, its services had been running on "99 per cent reliability".