Of today's 35 deaths, six people were from Northland, six were from the Auckland region, two from Waikato, one each was from Bay of Plenty, Lakes, Tairāwhiti, Hawke's Bay, Taranaki, MidCentral and the Wellington region, two were from Nelson Marlborough, nine from Canterbury, one was from West Coast, one from South Canterbury and one was from Southern.
"This is a very sad time for whānau and friends of those who have died and our thoughts and condolences are with them," the ministry said.
To date, 1841 deaths have been attributed to Covid in New Zealand, either as the underlying cause of death or as a contributing factor.
In the past seven days, an average of eight deaths have been confirmed each day as being attributable to the virus.
Covid modelling expert Michael Plank said the daily Covid deaths being reported were averaging at about 10 and he hoped that number would drop to single digits within the next month.
"Deaths are starting to come down now. Obviously, cases have been coming down for some time, deaths do lag behind so they would have peaked after cases did but it looks like they are starting to come down now," Plank said.
Today's figures show 402 people are in hospital and six people are receiving intensive care.
They are in Northland (seven), Waitematā (57), Counties Manukau (35), Auckland (52), Waikato (66), Bay of Plenty (17), Lakes (nine), Hawke's Bay (16), MidCentral (28), Whanganui (three), Taranaki (12), Wairarapa (six), Capital & Coast (15), Hutt Valley (12), Nelson Marlborough (eight), Canterbury (42), West Coast (four), South Canterbury (four) and Southern (nine).
The rolling average of cases today is 3496, down from last Tuesday's 4073.
For hospitalisations, today's average 453, compared with last Tuesday's average of 556.
Yesterday nine Covid deaths were reported. Four were from Auckland, two were from Waikato, one was from Canterbury and two were from Southern.
Dr Dion O'Neale, of Covid-19 Modelling Aotearoa, warned community case numbers – the lowest since the beginning of the country's first Omicron wave in February – needed to be viewed in the context of under-reporting.
O'Neale said a daily case number below 5000 was "on the lower side of what we'd expect".
The true number of infections in our community would almost certainly be higher – the figures reported by the ministry perhaps represent 40 to 65 per cent of cases – and under-reporting appeared to be a clear factor in some days' particularly low case counts.
"But, after experiencing these two peaks, we've also decreased the size of our susceptible population by quite a bit – and there's now fewer people remaining to be infected."