A second person has died while isolating at home with COVID-19.
The man, who was in his fifties, was found dead by ambulance staff at his Mount Eden home on Friday morning.
It's understood he was recently treated in hospital but discharged himself on Wednesday.
Deputy Prime Minister Grant Robertson said it is understood the man was admitted to hospital on November 1 before discharging himself on Wednesday.
He said the man spoke with health officials over the phone on Wednesday and Thursday.
"This particular person was admitted to hospital on the 1st of November and they discharged themselves from hospital on the 3rd. There was phone contact on both the 3rd and 4th of November and then there was an ambulance called this morning."
Robertson said his thoughts are with the man's friends and families.
"I want to add my condolences to the friends and family of the person who has passed away."
Both deaths reported this week are being investigated as part of a review by the Ministry of Health and Auckland DHBs.
The Deputy Prime Minister said he is confident in the self-isolation system which has continual monitoring.
"Between the Ministry of Health and Auckland Regional Public Health, they are looking at both these specific incidents but also the wider system. It's important to note there are still enquiries ongoing about the cause of death and I don't want to immediately assume what the cause of death is."
Robertson said two assessments are undertaken to ensure self-isolation is safe and practical before people are released to their homes.
It comes after a person died while isolating at home with COVID-19 on Wednesday. The exact cause of the first death is also unknown. The Ministry said it may have been COVID-19 or some other cause which will be determined by the Coroner.
The person was isolating at a Manukau address and was found dead by a family member visiting them on Wednesday.
The person tested positive for COVID-19 on October 24 and had been isolating at home with public health oversight.
There have been 28 deaths related to COVID-19 in New Zealand.