However a spokeswoman for Coleman said the protesters were overcooking what happened.
She said the ministers were not "chased" but had gone out the back door of the building as planned, to cross the road to the university's graduation parade.
The equal pay march was one of two protests in the city, the other about underfunding in the health system. The health protest was a silent vigil, however.
The drama followed the announcement of the new hospital - the largest build of its type in New Zealand's history.
Prime Minister Bill English and Health Minister Jonathan Coleman made the announcement at Dunedin Hospital this morning.
The new Dunedin Hospital will follow on from the completion of the new $77.8 million Grey Base Hospital on the West Coast, as well as the almost $1 billion hospital redevelopment programme in Canterbury.
Coleman said the Government had decided to rebuild in Dunedin at a cost of $1.2-$1.4b rather than refurbish the existing site.
The Ministry of Health was working to secure an appropriate site for the new hospital, with a strong preference for a central city location, he said. Depending on the location the new hospital would be opened in seven to 10 years.
"The original plan was to simply rebuild the services block, but the indicative business case has determined that the ward block also needs replacing and that has increased the cost significantly from the original $300 million estimate," Coleman said.
Given the size of the project, the Government would consider all funding options including a public-private partnership, he said.
There would also be steps taken to support the existing Dunedin Hospital while the rebuild took place, with an extra $4.7 million being invested into the Interim Works programme, taking the fund to $27.2 million.
"The programme includes the expansion of ICU to 22 bed spaces over the next 12 months. Taking the unit to eight ICU beds, 10 High Dependency beds and 4 beds which are flexible to be either as demand requires.
"The programme also includes the expansion of the Gastroenterology Unit, which will support the roll-out of the National Bowel Screening Programme to the DHB."
Coleman said it was a "once in a generation opportunity to build modern and sustainable health facilities that will meet the future needs of Dunedin and the wider Southern community".
English said the Dunedin Hospital rebuild was part of a commitment to "a world class health system".
The project was a "step that needs to be taken to provide the next generation of health services across the south".
"I know that this will be welcome news to people In Dunedin certainly but also... to the wider southern area."
"With such a large project we will want to ensure that it goes through the proper processes, not just around building but... defining services in a way that's going to meet the needs of this community through to 2040, 2050," English said.
It would be the largest hospital build in the country, he said. "In fact, short of some... of the very large transport projects, one of the largest construction projects in New Zealand."
"There's been a lot of pressure on southern health services, we understand that, we get to see it, I saw it in the patients that I spoke to today and the staff who are working so hard to make this winter work," he said.
"And we just want them to know that it's not just the money but the will behind this project and the improvements that it can bring in their lives - we're determined to see a job well done and determined to see it through."
In the lead-up to the last election, outgoing Health Minister Tony Ryall said of an expected major upgrade of Dunedin Hospital: "I expect Cabinet will consider a business case next year and an announcement would be made then."
Ministry of Health and Treasury officials had been working with the Southern District Health Board to develop a business case, he said in May 2014. Upgrading Dunedin Hospital was "one of our next projects", following upgrades of hospitals in Canterbury and the West Coast.
