In a promising sign that New Zealand might have its COVID-19 outbreak under control, case numbers have dropped for the second straight day.

The 49 cases announced on Tuesday, all in Auckland, were down from 53 announced on Monday and 83 on Sunday.

Encouragingly, director-general of health Ashley Bloomfield forecast further drops in case numbers in coming days.

“Based on our updated modelling, the reproduction rate of the virus in this outbreak is now looking like it is remaining under one,” he said.

“This means cases will continue to decline and we are successfully breaking the chain of transmission.”

Despite the positive signs, Prime Minister Jacinda Ardern said there was still “hard work ahead” and Kiwis shouldn’t think the battle was won.

“I would ask Kiwis just to hold that thought. Every day for me is another step. A bit of progress. But it’s too early,” she said.

“I want to see sustained reductions over a period of time.

“It is good not to see some of those high numbers we were on only a few days ago. But it’s another step. We’ve still got a journey to go through.”

The total case number stands at 612 people, with 597 in Auckland and 15 in Wellington.

Some 33 Kiwis are in hospital, including eight who are in a stable condition in intensive care.

The outbreak was emerged on August 17 but is thought to have been in the community at least a week prior.

While health officials have identified the index case as a returned traveller from Sydney who checked into quarantine on August 7, they still have not confirmed how the virus slipped into the community.

Ms Ardern said she was as eager as anyone to discover the leak.

“I lie awake at night thinking about them and I’ve not yet come up with any additional theories,” she said.

“Dr Bloomfield is smiling because he’s had to endure me listing off my new theories.

“We’ve investigated a number and have not yet identified the source. We’re left with theories that don’t have people to people contact but simply the air.”

New Zealand completed a fortnight in lockdown on Tuesday. It will begin to loosen restrictions for places outside Auckland from Wednesday.

From Wednesday, South Islanders and Wellingtonians will be able to get takeaway coffee and food, and essential workers will be able to use childcare.

NZ’s outbreak-prompted upswing in vaccinations also continues.

About 76,000 Kiwis were administered a dose of Pfizer vaccine on Monday – about 1.5 per cent of the population.

NZ remains behind Australia and the rest of the OECD in its vaccine rollout.

About 23 per cent of Kiwis (1.18 million) are fully vaccinated, with 44 per cent partially vaccinated (2.23 million).

Eligibility will finally be extended to under 30s on Wednesday, removing the final hurdle to getting vaccinated.

-AAP