There are 27 people who have recovered, Bloomfield said.
Seven people are in hospital and are stable; three in Wellington regional hospital, two in Nelson hospital, and one each in Waikato and Northland hospitals.
None are in ICU.
Most cases are still linked to overseas travel or to existing clusters of confirmed cases, but there are several suspected clusters of community transmission.
• Marist College in Auckland • the World Hereford cattle conference in Queenstown • a wedding in Wellington • a trip by a Wellington group of friends to the US • a contact with the Ruby Princess in Hawkes Bay that became infected and went to a winery • a rest home in Hamilton
More information will be provided about those clusters when available.
Yesterday 2417 tests were processed nationwide, taking the total number of tests to 12,683. About 1400 tests have been done daily in the last week.
People who have been tested must self-isolate from those in their household while awaiting the results of their tests.
Bloomfield said the number of confirmed cases could peak in the thousands, but he hoped the turnaround point may be in 10 days - if people complied with the lockdown rules.
That was based on a number of models, which will be released once Ministers had seen that information.
"We will expect the number of cases to increase for at least the next 10 days. If we all do our bit, and we break the chain of transmission, slow the spread of Covid-19 and we will be able to get on top of this."
From later tonight, pharmacists will be limited to providing only one month's supply of prescribed medicines, or a limit of three months for the supply of oral contraceptives.
Pharmacists still able be to make exceptions to provide additional amounts where people live remotely or for individuals with a disability.
He added that there were no significant shortages at the moment, but the measure was a precaution.
"These are unprecedented times," he said.
He said PPE for health professionals, such as masks, were in good supply, and DHBs were working hard to make sure workers had the protective gear they needed.
But not everybody in a hospital needed to wear a mask at all times, as it depended on each case and how infectious that case might be.
Asked about nurses in the North Shore who have been told not to wear masks as it might scare patients, he said those matters were up to clinicians and DHBs but the Ministry of Health will be providing guidance.
"Measures to address immediate needs for PPE equipment are being taken with urgency. For example, later today we will be sending 600,000 masks to DHBs.
"We are also continuing to manufacture more masks in New Zealand, more than 200,000 produced each day, and source masks and equipment from overseas."
168 Kiwi travellers in quarantine
Police Commissioner Mike Bush said day one of the nationwide lockdown showed that most New Zealanders were complying.
He said the police had to ensure safety, and to ensure the country was sustainable.
"Stay home to stay safe. If we don't comply, the consequence of that is people will die."
Police were being "very visible" and initially were talking to people to educate, engage and encourage them.
Bush said New Zealanders returning home into Auckland Airport since 2am this morning were being triaged.
"If you have any symptoms, you will be taken by health people to a place of quarantine."
Hotels and motels near Auckland Airport were being used, he said.
"If you have a place to go, we will help you get there. If you have friends coming to pick you up, only one person in your bubble will be allowed to take you," Bush said.
He said 360 people had come through Auckland Airport this morning, and it had gone smoothly, notwithstanding a few "speed bumps".
Eight of those had been quarantined because they were symptomatic, while 160 were quarantined because they didn't have suitable plans to self-isolate.
Those who had been allowed to travel on would be visited by police to ensure they were sticking to those plans.
Services that were open but not essential were being closed by police, he said.
Crackerjack in Hamilton was visited by police this morning, but it is unclear whether it had been forcibly shut.
Bush made it clear that people driving to a park during the lockdown had to "keep it local", and people should not be driving "willy nilly" all over town.
Gunman's guilty plea
Bush also commented on the Christchurch mosque gunman pleading guilty and paid tribute to the courage of the March 15 victims. He said the admission this morning meant they wouldn't have to relive the events of that traumatic day.
He also praised the police and prosecuting team involved in the case.
On the guilty plea, he said it was a "very fast-moving piece", and police had empathy for the people involved.
Sentencing would happen when victims were able to attend, he said.
He said he could not comment on why the plea had changed to guilty today.
Some police resources would now be able to be redirected to help with the lockdown, he said.
The Alert Level 4 nationwide lockdown came into effect at 11:59pm yesterday, and police are on patrol around the country to ensure people are staying at home unless they have a valid reason to be outside.
Bush said this morning some people were not even aware that a nationwide lockdown had been ordered.
People breaching the lockdown rules could be warned and their details taken.
"If people won't comply, we do have the authority to detain them, take them to our place," and give them time to contemplate their decisions.
People will be prosecuted for "serious" breaches, and could be charged for obstructing police, which could see a six month jail term.
Prisoners at risk
Bloomfield said there was a risk of Covid-19 infections in prisons, and Corrections had a means to protect prisoners, including health screening of all visitors and a ban on face-to-face meetings.
Any prison was at high risk of a Covid-19 outbreak, he said.
Prime Minister Jacinda Ardern said yesterday that modelling suggesting the number of cases in New Zealand could reach the thousands before dropping.
A national state of emergency was declared yesterday, and a number of new laws were passed urgently to give effect to the Government's plans to combat the spread of Covid-19.
Ardern implored everyone to stay home unless it was for essential services.
"I have to reduce down my contact, you have to reduce down yours. Everybody has to now move into a space where they act like we all carry Covid-19. That's how we have to behave."
Ardern is expected to give a press conference at 3pm today.