The targets for 10,000 tests per day for a week, with about two thirds of those in Auckland, have been "more or less" met, Health Minister Chris Hipkins says.
Speaking at today's official Covid-19 briefing, he said testing would continue at the airports, ports and isolation facilities.
He said no decisions have been made on changes to alert levels yet.
Director-General of Health Ashley Bloomfield said anyone in New Zealand who had symptoms - not just in Auckland - should get tested. He said there had also been some surveillance testing of unsymptomatic people across the country.
Hipkins and Bloomfield earlier both spoke to the Health Select Committee.
Read back through live updates from 2 September.
National Party's health spokesperson Shane Reti had requested from the committee chair that Dr Bloomfield, Hipkins and senior health officials be called before the committee, a request that was backed by New Zealand First.
Commmittee chair, Louisa Wall, agreed and said it would invite Minister of Health Chris Hipkins and Bloomfield to appear.
"I have always considered this was a matter for the committee to decide. However, there wasn't previously a majority who wanted the Select Committee to resume."
During the March lockdown, an Epidemic Response Committee (ERC) was set up to enable the Opposition to hold officials and the government to account, while Parliament could not run as usual.
But this time, when Parliament was reconvened as a result of the election date delay, it was agreed the ERC would not need to be re-established.
Last month, the High Court ruled that some of the country's alert level 4 lockdown was unlawful in the beginning stages.