It was a priority to visit because the hospital build in the central city was an important project and she was aware of significant local concern, Dr Verrall said.
"I came to listen and understand the concerns," she said.
The Government has been under sustained pressure to explain, justify or scrap design changes, or cuts, announced just before Christmas.
The Dunedin City Council this week voted unanimously to establish a public campaign to make clear the council "will not accept changes that reduce the long-term capacity of the new Dunedin Hospital, or that compromise in any way the clinical services available to residents of the city and the wider region".
Dr Verrall said the project team remained ambitious about how much could be achieved.
Her itinerary included meeting Dunedin Mayor Jules Radich, Invercargill Mayor Nobby Clark and Dunedin city councillor David Benson-Pope.
"We emphasised again we want to see the new Dunedin Hospital delivered as promised, to the design specified in the detailed business case," Mr Radich said.
The Otago Daily Times asked city councillors if they had a message for the health minister.
Cr Steve Walker was sure there would be further substantial cost increases during the project.
"I’d like an absolute, water-tight assurance from the minister that in the event of further and inevitable cost escalations, that there is to be no repeat exercise around hospital redesign with the sole purpose of saving money," he said.
Cr Mandy Mayhem said the healthcare system was stretched.
"Cutting back on the original plan and design is in no way acceptable," she said.
