"All testing for people who have been in Melbourne is free under the Section 70 notice, regardless of whether or not people are symptomatic," the ministry said in a statement this afternoon.
"This includes for visitors to New Zealand. For testing locations in Auckland, visit Auckland Regional Public Health Service (ARPHS). For all testing locations nationwide visit the Healthpoint website.
"As of this morning, 2237 travellers and 178 air crew had returned negative tests. That represents 49.3 percent of this group.
"Many of the remaining 2302 test results are expected to be received today and will be reported on tomorrow. It's important to note that not everyone in this group will be tested in New Zealand as some are infants and others have already returned to Australia.
"Under the current Section 70 notice, travellers wanting to return to Melbourne are not permitted to do so until they have returned a negative test result.
"The Melbourne cluster reinforces the critical importance of everyone in New Zealand keeping a record of where they have been by scanning QR codes or keeping a manual diary of their movements. It can help contact tracers quickly find potential close and casual contacts if there is a positive Covid-19 case in New Zealand."
The ministry said the variant of Covid being found in Melbourne is the B.1.617.1 variant which was first reported in India. It is considered more infectious than the original variant.
"The typical symptoms to look out for include a new or worsening cough, fever (at least 38˚C), shortness of breath, a sore throat, sneezing and runny nose and/or temporary loss of smell.
"Some people may present with atypical symptoms, with or without typical symptoms. These include new onset of fever, diarrhoea, headache, myalgia (muscle pain), nausea/vomiting, confusion/irritability."
In Australia the state of Victoria is scrambling to trace a "mystery case" at a Melbourne aged-care facility.
On Sunday, there were two cases of Covid-19 in managed isolation and none in the community in this country.
One of the confirmed cases travelled from Lebanon and tested positive on day 10.
The other case travelled from Saudi Arabia and tested positive on day zero.
That brought the total number of active cases in New Zealand to 16.
Victoria's health authorities are "extremely concerned" about a new mystery case of Covid-19.
One of the state's five new Covid cases today was a worker at an aged-care facility in Melbourne's west.
Health authorities were trying to determine how the female healthcare worker at Arcare Maidstone, who lives in Altona, caught the virus.
She was asymptomatic and wore a mask when she worked shifts on Wednesday and Thursday at the aged-care home.
"The aged-care positive case is an extreme concern to us," testing commander Jeroen Weimar told reporters today.
"It is our most vulnerable and sensitive setting."
On Thursday, Covid-19 Response Minister Chris Hipkins and director general of health Dr Ashley Bloomfield announced that New Zealand's travel bubble with Victoria would be paused for another seven days.
That means people will not be able to travel between the two locations without the need to quarantine until at least 7.58pm on Friday, June 4.
The Ministry of Health confirmed 4626 people flew from Melbourne airport to New Zealand between May 20-25, compared to the initial estimation of 5000 travellers.
However, 89 people from Melbourne are yet to be found after an order to get a Covid test and self-isolate.
Less than half of the 4626 people identified have been tested and returned a negative result.
