Seventeen per cent of cases are still being investigated. Bloomfield says many of those are expected to be community transmission.
There were 2563 tests yesterday – that makes a total of 26,000 tests so far.
More than 4000 tests can be processed a day, Bloomfield said.
He said there are eight labs in New Zealand, with that number ramping up in the coming days.
Bloomfield said the Government was looking into what the criteria was for extending the lockdown – he said he will have more details on that soon, possibly by Saturday.
The Government's goal is to get the number of cases "right down" and when that happens, the lockdown level can be reduced.
This can happen in different areas of the country – meaning if the number of cases in Auckland, for example, drops rapidly the alert level in the region will drop.
Some 1.8 million masks have been distributed to DHBs recently.
A further 41 million additional face masks will arrive from next week, Bloomfield said.
There are 23 million pairs of gloves and 800,000 glasses in the country at the moment.
"Our ICU staff are all geared up… to treat additional people," he said, adding that there are only two people in ICU related to Covid-19.
Today marks a week since New Zealand went to alert level 4 and the country went into lockdown.
Police 'will enforce' lockdown rules
Police Commissioner Mike Bush thanked the New Zealanders who are complying with the lockdown rules.
But he also called out those who are not complying.
He said more Police staff have been deployed to encourage people to do the right thing – if that does not work, "there will be an enforcement follow-up".
More Police have been deployed to the Kaitaia region, where Lance O'Sullivan was critical of people flouting lockdown rules. There have been four, possibly five arrests of people breaching the rules, Bush said.
Today is Bush's last day in his role as Commissioner – he said he was "extremely proud" of the frontline staff helping with the Covid-19 response.
He confirmed he would be continuing in his role in the Covid-19 committee.
He said the police has to spend time getting the system right to make sure there is compliance so there is not people-to-people, and place transmission of Covid-19.
Monitoring Kiwis arriving from overseas
People who arrive at the border will receive a call from welfare to make sure they're okay, Bush said.
But now, those people will be texted by the Police asking if they consent to be monitored via their cell phone.
This was being worked through with the Privacy Commissioner, Bush said.
The country is moving from a "peacetime" distribution system, to a "wartime" distribution system.
He said there is only a small group of people where the message "stay home" is not sticking.
Officials continue to tell New Zealanders not to get too complacent and warn the number of Covid-19 cases will continue to rise.
Yesterday, Prime Minister Jacinda Ardern said the Government has ordered more Covid-19 testing.
And health officials are already heeding that call and are bringing on two more testing labs in the coming days, bringing the total up to 10.
This, according to Health Minister David Clark, will mean there will be the capacity to test up to 5000 people a day.
Speaking to media yesterday, Ardern gave young New Zealanders a stern lecture to follow the rules and said they were the largest group of carriers.
There have been isolated reports of people breaking the lockdown rules, Bush said earlier this week.
He said at the time there had been three arrests so far – he will update media on the new total today.
NeedToKnow3
Bush was in front of the Epidemic Response Committee this morning where he admitted the advice given to Kiwis about what they're able to do during the lockdown hasn't been clear enough.
He said he "absolutely agreed" that the country needs clarity around some of the lockdown rules.
Bush also revealed that people in non-managed self-isolation are now being asked to allow police to see their location on their phones to ensure compliance.
He was grilled about who made the guidelines and exactly when people would find themselves on the wrong side of the police.