The Ministry of Health says it has contacted 18 people who sat near a person infected with coronavirus on a flight to Auckland.
They are all in self-isolation and have not yet shown any symptoms of Covid-19.
The Director-General of Health, Dr Ashley Bloomfield, said there has been initial contact with the 18 people by either cellphone or email, but that efforts will be made to follow-up any emails with face-to-face contact.
The people are mostly in Auckland, but one is in Nelson and one is in Christchurch.
Dr Bloomfield said officials are also making contact with the remaining passengers on the flight as a precaution.
"Now we do know that the spread of any infectious agents in an aircraft is limited by the air circulation systems because they have excellent filtration systems in modern aircraft, so that this disease which is spread by droplets rather than aerosolised is only likely to spread to those in close contact."
The number of confirmed cases of the virus in New Zealand remains at one.
The infected person, a New Zealander aged in their 60s, travelled from Iran via Bali and wore a mask on the Emirates flight to New Zealand on Wednesday.
This person was admitted to Auckland Hospital and tested positive for Covid-19 on Friday, but is now stable and improving, three of their family members are in self-isolation.
Watch Dr Ashley Bloomfield's latest update on the response to Covid-19.
Dr Bloomfield said they are moving to ensure that every person who comes into New Zealand will get information about Covid-19 and what to do if they become unwell.
"So we are moving to have all airlines making in-flight announcements and to providing the health card with the arrival card while the flight is on its way to New Zealand. This will ensure everybody has that information, it will be available in a range of languages."
He said measures at the airport will remain to enforce border restrictions for those who have been in China or Iran.
Since late January, 136 tests for coronavirus have been completed in New Zealand and 11 cases are still under investigation.
Prime Minister Jacinda Ardern visited Auckland Airport today to see the border operations in place for Covid-19.
She said vigourous efforts had been made to contact the people who were sitting in the two rows in front and behind the infected person on the Emirates EK450 flight.
She does not believe there is need to set up safe havens in order to keep the coronavirus from spreading.
It has been suggested that areas such as Northland and Waiheke Island in the Hauraki Gulf would be ideal places for people vulnerable to the disease to remain isolated.
But Ardern said there is no need for those measures.
"For those who are querying issues like whether or not we isolate people on islands and so on, we have a very robust process to make sure we track and trace anyone who's had contact with someone who contracts coronavirus and to minimise any change of outbreak."
Ardern said New Zealand's only confirmed case of Covid-19 has been handled in a text book way.