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Under its plan, the country would reopen to the world at a vaccination rate of 85-90% of the eligible population - along with district health board and age-based milestones - or on 1 December, whichever came earlier.
At present, 67% of the eligible population is fully vaccinated.
Collins said today there was no reason why the target couldn't be reached.
"We need to get on. We've got now now around 80, close to 85, percent of people have had at least one vaccination. After a big effort to get people vaccinated. There's another six weeks to go. There's no reason why everyone can't get the rest."
All DHB areas would have to reach the vaccination rates under the plan, she said.
Regions such such as Taranaki, where it's being estimated it will take until the end of the year to reach 90 percent, would "just have to do it" by December 1, she said.
"Everyone will have to just get in there and put some huge effort in".
Asked what would happen if the country reopened and Māori vaccination rates remained low, Collins said: "I think the Māori population will want to get itself vaccinated, and we've already seen an uptake with some of the efforts we've seen recently."
Collins said not only is business suffering, but tens of thousands of people including vulnerable communities, were missing out on other important medical treatment.
"Māori are also missing out on the assessments for things like cancer, heart disease, and everything else, and we do not believe that we should have Māori being targeted in terms of being blamed for the lockdown continuing."
Covid-19 modeller professor Michael Plank from Te Pūnaha Matatini said a fixed date for ending restrictions was not a good idea.
"I think we need to be responsive to what's happening in terms of the outbreak," he told RNZ's Morning Report programme.
"We need to be guided by the number of people that we've got vaccinated, and the epidemiology of the outbreak and the number of cases, the load on the healthcare system.
"They will change over time, so we need to be able to respond to that."