He made clear that tests are free.
There have been 1217 Covid-19 cases in New Zealand, Bloomfield said.
He said the message from the WHO is clear: Stopping outbreaks comes down to public health measures.
He said an action plan regarding clusters in NZ's aged-care facilities will be released soon. The review was commissioned in April.
He is now canvassing a response and the action plan will be released today - including an outbreak policy for aged residential care.
"We will be getting onto that very quickly."
He praised those who worked with older people through the lockdown period.
Meanwhile, Health Minister Chris Hipkins again reminded New Zealanders about "constant vigilance".
"We have to keep our pedal to the metal," he said, when it comes to locking in gains the country had made.
He said New Zealanders can't afford to be complacent.
"We cannot afford for Covid-19 fatigue to set in."
He said every link in New Zealand's chain needs to be strong to prevent another outbreak.
Hipkins said every New Zealander needed to make small sacrifices, like signing in with the Covid app.
There have been 627,000 downloads of the app, and 82,000 posters put up, he said. Some 31,000 businesses and organisations are displaying them.
Hipkins will write to every mayor in the country, asking them to also ensure their local businesses and public facilities are displaying the QR codes.
Asked at what point making putting up QR posters will be become mandatory, Hipkins said: "We're not there yet."
He said he hopes to have more to say about new Covid-19 tracing technology on Thursday.
Hipkins said he wants the rate of testing to increase.
Going to a GP was still a barrier to some people getting tests, he said.
Because of this, the Government will be utilising more pop-ups across the country.
He said there was testing of hotel staff in MIQ facilities in Rotorua and Hamilton.
"It is happening."
The Government was aiming to have tests every two weeks for those in contact with people in managed isolation, he said.
At the moment, every staff member who deals with people in managed isolation gets symptom-checked every day before going to work.
Hipkins said no one working at Auckland's Jet Park Hotel - the main isolation facility - is working anywhere else.
The hotel - which houses the infected - has a dedicated staff.
"I'm very comfortable around the Jet Park," he said, adding that those people are professionals who know what they are doing.
"They are taking this very seriously."
On a new, quicker test being used in the UK, Bloomfield said the Government was looking into a range of testing methods but more work needs to be done.
Hipkins said if you leave New Zealand "you are essentially entering a hot zone; the rest of the world."
He said if you leave, you will come into contact with people who might have Covid-19.
Hipkins said one of the first thing he did when he became health minister was to "beef up" support around mental health issues, when it comes to people going into isolation.
He said the situation is now better than it was.
He said the Government had a discussion "very early on" about what could be done.
Hipkins said that before he was the Minister of Health, he did not use the Covid-19 app very much.
But that changed after he became the minister.
Hipkins and Bloomfield both said they have never used the social media app, TikTok.
Prime Minister Jacinda Ardern yesterday also urged New Zealanders against complacency.
She told Kiwis to "say yes to the test", as she revealed that some people are refusing a Covid-19 test.
The country was moved to alert level 1 with the expectation that everyone would maintain good hygiene, keep track of their movements, seek medical advice if they have symptoms and get tested if needed, she said.
But Ardern said it appeared that hadn't happened, so the Government was "dialling back up" the Covid messaging.
"We have seen, however, there is a bit of a sense that New Zealand is free of Covid and that vigilance isn't required. We still need people to be on guard," she told her weekly post-Cabinet press conference.
Bloomfield and Hipkins are expected to provide an update on this.
They are also likely to be pressed on issues to do with the once-mooted Australian travel bubble.
Ardern yesterday would not put a timeframe on it but suggested an increasingly uncertain situation in Victoria gave the Government cause for pause.
On Sunday, there were 671 new infections and seven deaths in the Australian state.
The situation has forced Melbourne and regional Victorian towns into a strict six-week lockdown and led to a state of disaster being declared in the state.
