Thirteen Kiwis who recently travelled to NZ from Melbourne have been referred to "people-finding services" because the Ministry of Health has not been able to contact them.

The 13 are among 4539 people who flew from Melbourne Airport to New Zealand between May 20 and May 25.

All of these travellers are being instructed to get a test and self-isolate at home - or in the accommodation they are staying in - until they have a negative result, the ministry said in a statement this afternoon.

There are no new cases of Covid-19 in the community in New Zealand today. There is one new case in MIQ, the ministry says.

The ministry says anyone who in Victoria since May 11 should keep checking the Victorian Government website because locations of interest were being continually added.

"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."