Of the new cases, 4630 are reinfections reports RNZ.
The ministry reported 24 deaths over the past week.
The ministry said 26 deaths were attributable to Covid-19. It said the change in total deaths with Covid-19 may not be equal to the number of new deaths reported today.
"This is because deaths that occurred more than 28 days after a positive test that are subsequently determined to be unrelated to Covid are removed from the total."
Of the 24 deaths being reporting today, one was from Northland, one was from Bay of Plenty, three were from Hawke's Bay, one was from Taranaki, two were from MidCentral, five were from Wellington region, one was from Nelson Marlborough, five were from Canterbury, one was from West Coast and four were from Southern.
Three were in their 60s, five were in their 70s, nine were in their 80s and seven were aged over 90. Of these people, 13 were women and 11 were men.
There are also 200 people with Covid-19 in hospital as of midnight Sunday, with eight cases in ICU.
The seven-day rolling average of cases is 1593.
Figures reported last week showed there had been 11,544 new cases of Covid-19 reported, and 12 deaths attributed to Covid-19.