A group of about 30 protesters chanting, carrying placards and wearing 'They save We pay" t-shirts were waiting to greet Mr Luxon at the entrance to the Dunedin Public Art Gallery.
But Mr Luxon's motorcade stopped instead in Moray Place, at the back of the art gallery.
Mr Luxon was seen walking briskly past a smaller group of seven protesters.
Protest organiser Cr Steve Walker said the Prime Minister's decision to not enter through the front, past protesters, was "cowardly" on his part but a win for the protesters.
"He's cognizant of the fact there is a voice in this city that he is unprepared to face up to and speak to and explain his side of the story ."
It was "completely inappropriate" for a Prime Minister to not face up to protestors -- who just wanted answers to "fundamental questions".
"He is the man in the position, along with Dr Reti, who can give us those answers".
Mr Luxon is visiting Dunedin to take speak and present certificates to young achievers at the Otago Daily Times' Class Act event.
in the Octagon Noeline Speight, of Brockville, said the hospital was "very important" as it was a teaching hospital and was used by children.
The current hospital had leaking walls and was used to service the whole southern region.
Sam Sharpe, of North East Valley, was protesting the cuts to the new Dunedin hospital.
He was one of the estimated 35,000 people who turned up to the council-led protest in the Octagon recently.
The longer the government waited to build it, the more expensive it would be, he said.
"Just keep your promises."
Cr Walker has been leading calls for locals to make their feelings clear about government plans to shrink the new hospital.
"We need to make sure our voices are heard," he said in a Facebook post.
