A poll conducted by Kantar and published by The New Zealand Herald shows 85 percent of Kiwis support the elimination goal, compared with 13 percent arguing to "live with" the virus.
Of that 85 percent, 46 percent support elimination long-term, while 39 percent support elimination until 70 percent of the population is vaccinated.
The support for elimination is largely consistent across demographic and regional breakdowns.
Showing the resilience of Aucklanders - currently in the middle of their fifth lockdown - 87 percent of residents in New Zealand's biggest city offered their support to elimination.
Wellingtonians (91 percent) are the most likely to support elimination, with Cantabrians (84 percent) the least likely.
Meanwhile, in recent days, senior Australian politicians have attacked the elimination goal.
Prime Minister Scott Morrison has called enduring support of elimination "absurd" and on Wednesday, Treasurer Josh Frydenburg took aim.
With more than 100 cases yesterday in Victoria, Mr Frydenburg said elimination was out of reach.
"I welcome the acknowledgement in Victoria today that eliminating the Delta variant is an impossibility. It can't be done. No other country has done it, and based on the best medical advice we have we can't do it," he said.
It remains to be seen whether New Zealand will prove the pair wrong in coming weeks.
On Thursday, New Zealand reached day 16 of a national lockdown, launched after the identification of one case, to fight its first Delta outbreak of Covid-19.
The Director-general of health, Ashley Bloomfield, says he is confident the peak of the outbreak passed on the weekend, when 82 and 83 cases were announced.
Since then, 53 cases were announced on Monday, 49 on Tuesday and 75 on Wednesday.
Thursday's case numbers will be announced at 1pm.