People were also reminded to follow strict Level 2 rules of wearing a face mask, practising social distancing and tracking your movements using the Covid-19 tracer app or personal diary.
"There are multiple options for testing across the region so it is important anyone gets tested, however mild their symptoms and even if they are vaccinated," he said.
More than 250 people were tested on Sunday but expected more people to be testing over the next few days.
The case, from Auckland, remained in isolation at Kennedy Park Resort, which has been set up for such purposes and which housed dozens of people without accommodation after the Napier flood on November 9 last year.
The affected man, who travelled from Auckland to Hawke's Bay apparently unaware of a Covid infection, late on Monday remained the only notified case in the Bay.
The Ministry of Health confirmed in a 1pm statement there were no new Covid-19 cases to report in the region on Monday, but two Hawke's Bay police officers were isolating after coming into contact with the man, as were three pupils of a Napier primary school.
There had also been no release of locations of interest name in connection with the man who had been tested in Auckland but was in Hawke's Bay by the time he was advised the result was positive.
The two police officers had returned negative results from their day one tests, a Ministry of Health spokesperson said.
Onekawa Primary School principal Steve Bloor confirmed the isolation of three pupils, saying they had also returned negative results after being identified as contacts of the Covid-19 positive case.
"It was a bit of a shock when I heard about the connection," he said.
On Sunday, DHB Medical Officer of Health Dr Rachel Eyre said the person was tested before leaving Auckland and received the news of a positive result after arriving in Hawke's Bay.
The person had permission to make the trip from Auckland, according to a statement from the DHB on Sunday, and was currently isolated at Kennedy Park, a community isolation facility.
The DHB said initial test results of identified close contacts had returned negative for Covid-19, but more testing was being processed with urgency.
No locations of interest have been posted in the region, as of Monday morning at 10am.
Bloor had been in touch with both the Ministry of Education and Ministry of Health on Saturday evening and throughout Sunday, both of which had assured him the children were safe to return to school today.
He said it was "business as usual" at the school and there had been no deep cleaning over the weekend, with no significant absences as a result.
He said the school community had been really supportive and he was proud of staff, all of whom were vaccinated before the Covid-19 vaccine mandate came into effect.
"All in all the situation has been really well managed. We've got really good safety protocols in place."
With four weeks left before school finished, Bloor said he was feeling positive about the remainder of the year.
The Salvation Army Family Store in Napier's Carlyle St remained closed for deep cleaning on Monday.
A spokesperson for the group said this had not been requested of it by Public Health but had been undertaken on its own initiative.
"There has been speculation that a positive Covid-19 case visited the store, but, to our knowledge, this is not the case."
She said the group had spoken to Public Health on Saturday who was undertaking its own investigation.
"They said at this stage there is no reason to believe a positive Covid case has been in the store. They have not advised us to close."
Police are working together with the Ministry of Health on the circumstances in which the Covid positive person left Auckland for Napier.
The spokesperson said the ministry was working with health agencies on the circumstances around the person's departure from Auckland.
"At this stage there is no further information or comment we can provide."
