Thursday's seven-day rolling average of case numbers is 7705, down from 7935 last week.
There are 484 people in hospital with the virus - with 15 in ICU.
The 13 deaths reported yesterday included people who had died over the previous nine days, apart from two deaths on 4 April. The Ministry of Health said 723 people with Covid-19 had now died in New Zealand.
Two of today's deaths were from the Auckland region, three from Bay of Plenty, two from Waikato, one from Taranaki, one from MidCentral, one from Hawke's Bay, and three from Canterbury. Two were in their 50s, two in their 60s, one in their 70s, three in their 80s, and five were over 90. Five were women and eight were men.
There were also 80 new cases of Covid-19 detected at the border.
New Zealand has now recorded a total of 912,490 cases of Covid-19.