However, he pointed out that elimination never meant zero – "but it does mean we know where our cases are coming from".
He said that the Government's goal has been elimination, not eradication – whereby the virus is completely stamped out in New Zealand.
"If you think about alert level 4, I would say we have achieved, through alert level 4, the position we wanted to be in so that we could now start to, move down alert levels."
Ardern was also optimistic – asked if New Zealand had eliminated Covid-19, she replied "currently".
But she pointed out that the next challenge for the Government was Covid-19's tail.
"Elimination means we may well reach zero, but we may well then have small numbers of cases coming up again," she told media this afternoon.
"That doesn't mean we have failed, it just means that we're in the position to have that zero-tolerance approach to have very aggressive management of those cases and keep those numbers low."
Bloomfield said he was confident New Zealand can go into alert level 3 safely.
Ardern said NZ was 11 hours away from leaving the "strictest" constraints in NZ's modern history.
"We did. And we did it together."
She praised Bloomfield: "I think we are lucky to have a public servant of Dr Bloomfield's calibre leading the health response and I have very much enjoyed sharing a podium with you."
The person who died was a woman in her 90s at St Margaret's Hospital.
She had a number of underlying health conditions and was the third person in that cluster to die.
She was the 19th person to die from coronavirus-related causes in New Zealand.
Waitematā DHB released a statement following the death.
"The thoughts and prayers of Waitematā DHB's staff and management are with the patients family and friends at this difficult time. We are all saddened by their loss and ask that the family's privacy is respected as they mourn the passing of their loved one."
Bloomfield said the Government was looking into testing changes it can make in terms of aged residential facilities - not just for the residents, but also staff.
In terms of the new cases, one is new and four are probable cases.
Three are linked to St Margaret's Hospital, with two linked to other cases.
Six cases that were probable have been reclassified, meaning the national total is 1469.
Bloomfield said some public health units were reviewing some probable cases and that was why some classifications have changed.
The ministry would continue to do this, he said.
There is only one case in New Zealand that is still being investigated.
Bloomfield said the case was in Tauranga and while there was a "strong suspicion" of a potential link, it had not been confirmed.
In response to a request for further information about the case, including when they tested positive and how many people were working on the investigation, a Ministry of Health spokesperson said no further information about the individual would be released at this stage.
It's something officials are working on, she confirmed.
She said it was "very likely" that NZ citizens in Australia can come home soon.
"That is something we can consider," she said, but added it needed to be done safely.
Asked if marae could be used to house some people who were homeless at the moment, Ardern said the Government would continue to work with Māori on this issue.
Bloomfield said hospitals in level 3 would start easing into elective surgeries.