Pasifika Medical Association chief executive Debbie Sorensen said when rollout goes wider, consideration should be given to putting South Auckland near the top of the queue.
The area's many border connections put it on the Covid front line.
"Our border is not in Remuera or the North Shore, the border is in South Auckland. The airport is based in Māngere and, of course, a high number of people that are working on the border and the quarantine facilities live in South Auckland," Sorensen said.
The area was doing more than its fair share to keep the country safe and had a higher proportion of people more likely to be hit hard by the virus, she said.
RNZ understands the Ministry of Health has discussed a targeted vaccination campaign for South Auckland but has not yet made a decision.
An earlier rollout would not need to come at the expense of the rest of New Zealand, Sorensen said.
"We're so efficient as a country in terms of being able to roll out vaccination programmes that it won't be that long before everyone else will also have access to the vaccine, so there is definitely a case to be made," she said.
A co-leader of Te Rōpū Whakakaupapa Urutā, the national Māori Pandemic group, Rawiri Jansen, said he regularly saw families of border or frontline health workers in his job as a GP in Papakura, and Covid created significant anxieties for them.
Though vaccinating South Auckland would have a benefit both for those living there and the rest of the country, he hesitated to use the word "prioritise", saying other parts of the country had MIQ hotels, ports and vulnerable people too.
Their needs must also be weighed up, he said.
"There is no ethical prioritisation that says somebody with comorbidities living in South Auckland is more important than someone living with comorbidities in Northland or East Cape ... but we can describe sequencing this, doing it in order, so we keep the whole community better protected," he said.
The Government had so far ruled out vaccinating those connected to the Papatoetoe outbreak.
That was despite one scenario in its current roll out plan that said a community connected to a controlled outbreak would be vaccinated.
Covid-19 Response Minister Chris Hipkins said the Government was sticking with its plan to prioritise border workers and the most at-risk frontline workers.
The second batch of the Pfizer vaccine, enough for 33,000 people, arrived on Wednesday and similar amounts are expected to arrive weekly.
- RNZ