Bloomfield said the people travelled to Tokoroa when they were feeling in good health.
South Waikato Mayor Jenny Shattock had last night told staff: "Unfortunately we have a confirmed case of Covid in Tokoroa and a probable case, plus five others have been tested as some of them are unwell.
"At this stage we have [a doctor] in isolation and the nurse who swabbed the patient plus a council staff member is isolating as well." Tokoroa is a town of more than 13,600 people.
The Tokoroa Family Health today confirmed a patient at the practice had returned a positive test.
The infected person was a close contact of a person in the Auckland cluster who had visited whanau in the Waikato township.
All appropriate precautions were taken during the testing with health staff in PPE.
After the confirmation of a positive result, staff had worked late into the night to test other close contacts of the infected patient.
The clinic was now closed for a deep clean. All staff were swabbed and awaiting test results.
Meanwhile up to 300 people who attended a Māngere East church on Sunday have been urged to get tested for Covid-19 urgently after a family at the congregation tested positive.
Everyone who was at the Congregational Christian Church of Samoa Māngere East Puaseisei on Sunday and anyone who has been in contact with them are being told to get a test as a precaution.
Health officials confirmed late last night that a preschooler had tested positive for the virus.
The youngster is a pupil at the Taeaofou i Puaseisei Preschool on Winthrop Way, Māngere East, opposite the church. Many of the church's youngest members attend the preschool.
Reverend Victor Pouesi said the church was supporting the family involved after several members - including the preschooler's parents and at least one other child in the family - had tested positive for Covid-19.
"It's unfortunate this has come up and we don't really know who's [possibly] got the virus.
"We're all working together to solve this problem. It's really hard to track and trace, so we've told everyone to get tested."
The church is made up of 90 families - up to 500 to 600 people. But up to 300 people attend a usual Sunday service.
Speaking to the Herald this morning, Pouesi said he understood that one of the preschooler's parents works with a family member of one of the initial family-of-four confirmed to have Covid-19 this week.
He confirmed the preschooler and their family had been at church on Sunday and that he himself had come into contact with at least one of them.
"After church, I always greet and shake people's hands - and I think I shook the mother's hand. We - my own family - are booked to go get tested today."
The church has two preschools - the other on nearby Raglan St - and both have been shut down as a result of the confirmed case.
Child not at school when they had symptoms
Health officials have advised the church and staff that the child involved, a pupil at the Winthrop centre, did not go to school when they had symptoms.
As a result, it was considered a "low risk" that other children and staff had become infected.
It was still, however, worth shutting down and getting everyone tested.
Pouesi said their administrator tasked to contact all the children's families had reported that no one connected to either preschool centre had shown any symptoms so far.
The church minister said he had spent the past few hours offering pastoral care to the family involved and members of his congregation; calling for calm and support for each other.
"This is not the time for blaming. We have to pray for everyone and remember there is something more precious at stake - the lives of our people we need to protect.
"I believe there's always God watching over us. We are dealing with an invisible enemy."
Southern Cross confirm case
The principal of South Auckland's large Southern Cross Campus said a child in its junior school had tested positive for Covid-17.
The primary pupil was withdrawn from school earlier in the week when they fell ill and the family was tested.
Samantha Smith said she was contacted by the Auckland Regional Public Health Service last night confirming a pupil was infected.
She said the school would be closed for the next 72 hours and those who were most at risk would have been contacted by the Ministry of Education or public health service.
Smith praised the family for taking immediate action when they started to show symptoms.