New Zealand has 76 new cases of the novel coronavirus (COVID-19), bringing the total of confirmed and probable cases to 589.

The latest figures were announced by the Ministry of Health's Director-General of Health Dr Ashley Bloomfield during a press conference on Monday.

One formerly probable case is now among the 76 new confirmed cases. There are no other probable cases as of Monday, with the total of probable cases standing at 37.

As of Monday, 63 people have recovered from the virus in New Zealand. Twelve people are currently hospitalised with three expected to be discharged soon. Two of the hospitalised patients are in the ICU.

The average daily test number is sitting at 1728.

There have been no additional deaths related to the virus since Sunday.

Of the 455 cases where the ministry has sufficient information, 57 percent have a direct link to overseas travel, 26 percent are close contacts of existing cases, 15 percent have both overseas travel and/or close contacts as factors and 2 percent - roughly 10 cases - are due to community transmission.

Dr Bloomfield said the flu vaccine is now imperative to the overall COVID-19 response. People over 65, pregnant women, children with respiratory illnesses and frontline health staff are the priority.

Police Commissioner Mike Bush acknowledged the vast majority of New Zealanders are complying "brilliantly" with the Alert Level 4 lockdown measures.

• The Netherlands has recalled 600,000 coronavirus face masks it imported from China after discovering they were faulty
• First New Zealand death recorded
• How to shop safely on digital marketplaces during the COVID-19 lockdown
• China essentially treats Australia ‘like a shopping mall’

He confirmed three people have been arrested for "persistent breaches" of lockdown protocol. Two have been released without charge while one remains in custody.

There has been a "very slight reduction" in family violence and family harm reports nationwide over the last few days, Bush said, noting a "massive decline" in public displays of violence as expected. Police are now putting their efforts into ensuring lockdown compliance.

Two police officers have tested positive for COVID-19 and remain at home. Neither require hospitalisation.

Bush reiterated the importance of social distancing during lockdown. New Zealanders are permitted to take exercise in their local area but must maintain a two-metre distance with others.

Death toll remains at one 

On Sunday, New Zealand's first coronavirus-related death was announced. The deceased was Anne Guenole, a West Coast woman in her 70s. Guenole died at Grey Base Hospital in Greymouth on Sunday morning. 

It was revealed that Guenole, who had an underlying health condition, was initially thought to be suffering from influenza when she was hospitalised on Wednesday. It wasn't until Thursday night that Guenole met the criteria of a COVID-19 case. 

Twenty-one West Coast District Health Board (WCDHB) staff are self-isolating as a precautionary measure. Medical staff who assessed Guenole were wearing the suitable PPE (personal protective equipment) for treating an influenza patient, but were not wearing the eye protection required for a possible or confirmed COVID-19 case.