Health authorities were reviewing the details of the three confirmed community cases in New South Wales in the past 24 hours and a fourth case that was under investigation.
Many locations of interest have been identified in the Australian state.
The Ministry of Health was also contacting people who had travelled from Sydney to New Zealand since June 11, advising them to check the locations of interest, and to self-monitor for symptoms for the virus.
Anyone who developed symptoms should self-isolate and get tested.
People in Australia who had been in a location of interest at the specified time should follow state government advice for isolation and testing, and cannot travel to New Zealand within 14 days from when they were at the location of interest.
McElnay said the ministry was taking a cautious approach as investigations continued and quarantine free travel with New South Wales would be under constant review.
Kiwi health officials were monitoring a range of factors - including whether any new cases are identified, and the results of Covid-19 testing of contacts and from the wider Sydney community.
"Border controls are a key tool for stopping the introduction and spread of new cases from overseas and remain central to our elimination strategy," McElnay said.
"We remain in close contact with health officials in New South Wales and will continue to closely monitor the situation. Updates will be provided if there is any change to this latest advice."
It comes after New Zealand health officials extended a travel pause with Victoria for another five days - as the number of cases associated to the outbreak in the greater Melbourne area reached 100.
The pause was originally in place until 11.59pm this evening, but Covid-19 Response Minister Chris Hipkins said a short extension to 11.59pm Tuesday was "in line with our precautionary approach".
