It comes after the hospital’s emergency department was shut down overnight due to a lack of staff earlier this month.
Minister of Health Dr Ayesha Verrall will meet Waitaki District Mayor Gary Kircher, Deputy Mayor Hana Halelele and Waitaki Health chief executive Keith Marshall in two weeks to discuss the needs of the hospital and clarify its status in the health system.
Mr Kircher said he was concerned by a comment made by Dr Verrall recently, where she referred to the hospital as owned by a community trust.
Although the hospital existed as its own entity, it was still a public hospital, he said.
"It doesn’t matter who owns the hospital, the Waitaki District still deserves the same level of care."
In the 1990s it was proposed Oamaru’s hospital be shut down, as it was too large and became a liability.
Negotiations between local government and the active health authority at the time resulted in a new hospital being built, which would be owned by the council.
Although it was not run by health authorities, the hospital would be public, not private.
As time had gone on it had been treated by health authorities as private, Mr Kircher said.
It was a result of a "loss of institutional knowledge" which developed as health authorities changed and key figures left.
"They don’t feel an obligation to help.
"The original promise has been overlooked."
Te Whatu Ora’s main goal was to deliver core healthcare, which was what Oamaru Hospital was designed for as well.
The council’s relationship with Te Whatu Ora had been "really positive," but it still needed support with vital aspects, such as filling doctor and nurse positions.
In March this year Te Whatu Ora increased its funding for Oamaru Hospital by $3.5 million.
That money was welcomed and used well to help keep staff on board, but there was a nationwide shortage of medical staff and Oamaru was "stuck in the middle" of larger centres, Mr Kircher said.
If the hospital was forced to shut down its emergency department due to a lack of staff, Te Whatu Ora should be able to work with Oamaru Hospital to ensure it kept running, he said.
This could mean sending staff to Oamaru for the night.
"Fundamentally it needs to work in conjunction with other hospitals."
Oamaru Hospital was doing its best to recruit more staff, but it was not able to fill all the required shifts.