Ardern reiterated calls for people to take up free immunisations and stay at home if they were experiencing symptoms.
In Auckland, about 50 schools and a similar number of early childhood centres have had confirmed cases this year with hundreds more pupils potentially exposed after an infected student went to the St Peter's College school ball over the weekend.
Bloomfield said decisions about specific events fell with organisers.
The number of cases has been growing at about 18 or 19 a day in Auckland and it is the largest outbreak since the 1990s by a significant margin, coming amid falling vaccination rates since about 2015.
Bloomfield told reporters on Monday that despite ongoing discussion about the effect anti-vaxxers were having, experience from the 1990s had shown those who completely opposed vaccinations were fewer than 5 per cent of the population in most centres and high immunisation rates could be achieved amid vocal opposition.
"When we had had low vaccination rates through the '90s and into the early 2000s, we put in a huge effort … and we got very close to 95 per cent [coverage]," he said.
"The gap between 90 and 95 is not an issue of opposition; it's an issue of access and really good information."
Meanwhile, pharmacists and the National Party have also been calling for the Government to change rules to allow chemists to administer the measles vaccine.
There are 864 pharmacists around the country who are allowed to give vaccinations for the flu, shingles, whooping cough and meningitis, but current rules mean they don't get funded to provide the MMR (measles, mumps, rubella) vaccine.
The Pharmaceutical Society of New Zealand says its members could play a role in helping improve vaccination rates.
In a statement, Associate Health Minister Julie Anne Genter said she had asked the Ministry to look into the matter.
But Ardern said there were a number of issues to be worked through on the suggestion, including opening up the national immunisation register to pharmacists.
"But we need to ask: are people currently unable to access immunisation?" she said.
"Are pharmacists needed in addition to [current efforts]?"
In a statement, the Ministry of Health said it was urgently exploring what role pharmacists could play in helping improve the uptake of the MMR vaccine.
"There are some issues that need to be worked through before MMR is available in community pharmacies, such as funding, reimbursement, classification and record keeping," a spokesman said.
The Ministry had put additional nurses into communities, particularly in Counties Manukau, and 25 more nurses were currently being trained, Ardern said.