The review is expected to cover problems including treatment delays and funding within the department.
Although he acknowledged action was needed to address the 10 "significant urological" surgeries, Fleming said no one knew when it would be possible to perform them.
"We're going to be meeting sometime next week to try to identify how we can come up with sustainable solutions to address it."
The urological department is the latest blight on an increasingly unhealthy-looking Dunedin Hospital.
There are significant delays for general and plastic surgery, and a shortage of intensive care unit (ICU) beds has cancelled some cardiac operations.
The ophthalmology department is continuing to clear a backlog of about 3500 patients.
Fleming said it did not take much for the hospital system to become unstable, and said the junior doctor strike in January had "thrown the system out of sync". It had been struggling to catch up since.
Labour's Dunedin North MP David Clark said the situation at the hospital was dire, and getting worse by the day.
He said the hospital building is also leaking, which is cancelling surgeries.
"And now there is internal spouting on the first floor of the building because rain's coming in at the eighth, and it's making it that far down through the internal walls."
Clark said Dunedin Hospital was "emblematic" of the government's neglect towards the South Island over the past nine years.
"Even in 2015 they were saying a hospital would be seven to 10 years away, meaning it could've been finished by 2022.
"Now they're saying 2027 is the earliest it could be here, so that's now five years away than it could have been two years ago. That's unacceptable."
Regardless of the election outcome next month, Clark, Labour's health spokesman, wanted construction of the hospital to begin within the next three-year term.
"The public just want reassurance that no matter who's in government, the hospital will be built."
Fleming agreed.
"We've got a system that is under significant stress and pressure. Dunedin Hospital is in bad need of redevelopment."