The first case is a woman in her 20s who arrived in New Zealand on July 3 from India. She has been staying in managed isolation at the Stamford Plaza in Auckland.
The second case is a man in his 30s who returned on July 4 from Italy. He is staying in isolation at the Commodore Hotel in Christchurch.
The third case is a man in his 20s who arrived in New Zealand on July 3 from India. He has been staying in isolation at the Stamford Plaza in Auckland.
It has been 69 days since the last case of Covid-19 was acquired locally from an unknown source, the Ministry of Health said.
Two previously reported cases have now recovered, which brings the total number of active cases to 24.
"There is no one in New Zealand receiving hospital-level care for Covid-19," the ministry said.
"Yesterday our laboratories completed 3,089 tests. That brings the total number of tests completed to date to 422,144."
One new case yesterday
Yesterday there was one new Covid-19 case in New Zealand, a man who had escaped from managed isolation at the Stamford Plaza hotel in Auckland on Tuesday night and went walkabout for 70 minutes, including visiting a Countdown supermarket. He tested positive the next day.
Earlier today the Government minister in charge of managed isolation, Megan Woods, told RNZ there could be more police involvement in managing those in 14-day isolation.
"Only one group of people have the power to detain, and that's the police," she said.
She also signalled restricting the use of outdoor areas while there was construction happening.
"It's probably not appropriate to have someone in a smoking area when there's contractors on site and where it's not clear who's who. We're reviewing all of those things and we'll have more to say on that later today."
Yesterday temporary barricades were replaced with six-foot high fencing at all isolation and quarantine facilities across New Zealand.