Asked if there was anyone who has refused a test while in isolation, Bloomfield said he was not aware of anyone who had.
All guests now being tested on day three of managed isolation
A total of 3402 Covid tests were completed yesterday.
More than 500 tests were also conducted at managed isolation facilities across the country, Bloomfield said.
Everyone at a managed isolation facility was now being tested at day three of their stay.
Those staying in hotels should not have contact with anyone else, he said.
The beginning of the isolation was where the enforcement was the strictest.
With Auckland hotels reaching capacity, Bloomfield said the defence base at Whangaparaoa and the use of campervans to house travellers was under "active consideration".
Part of the reason people are being found to have Covid-19 now was because the Ministry of Health was doing a lot more testing, he said.
In the past, he said there could have been those that did not report mild symptoms - that's why the testing at day three of isolation was so important.
Bloomfield said questions were being asked about what was happening when it came to screening of people before getting on flights.
Over the next couple of days, some 900 people will be coming to New Zealand from overseas.
Bloomfield said much of the morning was spent talking about these issues.
It was agreed that protecting New Zealanders was "paramount".
In addition to this, Covid-19 was spreading overseas so it made sense to see more cases when people were coming to New Zealand.
A lot of effort was being put into having the tests done at day 12 of isolation, so the guests could have the results the next day and be allowed to leave on day 14.
New Zealand's sea borders, and how these were to be managed, was being discussed at Cabinet today.
Bloomfield would not say what his advice to Cabinet was - saying he would prefer to leave that to ministers.
Novotel Ellerslie guests test negative after UK sisters' road trip
Bloomfield said that since June 9 there were 55 people granted compassionate exemptions to leave managed isolation facilities - 54 of those cases had been followed up. Fifty of them had tested negative and four children were not tested.
Everyone at the Novotel Ellerslie hotel where the two British sisters had stayed before driving to Wellington had now been tested and the results were negative.
There were 190 people who had been guests at the hotel, 179 of those have been contacted and 156 of them returned a negative result.
The remaining 11 are being followed up.
Bloomfield said there is "extensive" work being done to contact every one who left between the 9th and the 14th of June to see if they have been tested.
That work is expected to be finished by the end of today.
In terms of the other cases confirmed over the past few days, Bloomfield said they are being followed up with as well.
Last night reports emerged that another person had tested positive at the Auckland Airport Novotel hotel while in managed isolation. Guests said they had been told to stay in their rooms and that food would be delivered.
Prime Minister Jacinda Ardern would not confirm an eighth active case this morning, saying it was for the ministry to provide the numbers.
Hotel guests told to say in their rooms
The Herald understands a person staying at a Novotel in Auckland tested positive on Sunday night and the hotel is now in full lockdown.
Auckland Airport's Novotel says it's waiting on information from the Ministry of Health about how long the lockdown will last. Photo / RNZ, Alexa Cook
Alexa Cook, who has been in isolation at the Novotel Auckland Airport since June 13, said she was also informed of the new case at 8.25 on Sunday night.
"We had a call to our hotel room from reception and it was a guy from the New Zealand Defence Force saying, 'please stay in your room, the hotel has gone into full lockdown because there's been a positive Covid-19 test from inside this hotel'."
If confirmed, this would be at least eight active cases in New Zealand, all from managed quarantine facilities.
Yesterday, the Ministry of Health confirmed another two cases of Covid-19 – one is a child under two.
In that case, it is the child a Covid-19 positive couple who have recently arrived home from India.
The second case is a 59-year-old woman who travelled from Delhi, arriving in Auckland on June 15 on flight AI1316.
Both cases were recent arrivals from overseas and both were detected within managed isolation facilities.
"These cases show the managed isolation system working as it should," Cabinet Minister Megan Woods – who was taken charge of the Government's isolation and quarantine operations – told media yesterday.
She stressed that as Covid-19 gets worse overseas, more New Zealanders will be looking to come home – "so there is no room for error".
Air Commodore Darryn Webb, who is in charge of the operational side of the isolation and quarantine operations, confirmed yesterday that there are almost 4300 people in managed isolation across New Zealand at the moment.
