Auckland Mayor Phil Goff says the whole city should be prioritised for the Covid-19 vaccine rollout, over other parts of the country that are at less risk.

Goff welcomes the government's indication that South Auckland will be prioritised, but he says the rest of the city should follow.

"Auckland's fourth level 3 lockdown highlights the fact that the city is at greater risk of community transmission than any other city or region in the country," he said.

"As the gateway city to New Zealand, and with 18 quarantine facilities - significantly more than the rest of the country combined - Auckland carries the burden of risk on behalf of the country.

"Protecting Auckland will help ensure that we stop the disease from being transmitted to other parts of the country."

Goff says Auckland loses an estimated 200 jobs and $30 million a day under level 3 restrictions.

"The roll-out of vaccines for frontline workers started in Auckland which was absolutely the right thing to do. Now I would like to see that continue for the rest of the city," he said.