Pilots have been pushing for compulsory face masks on international flights as a way of encouraging more people to fly.
New Zealand's Covid-19 free status was scrapped earlier this week when two women from Britain tested positive for Covid-19, and it was revealed that they had received a special exemption to leave managed quarantine to see a dying parent. The pair drove from Auckland to Wellington and tested positive when they got to Wellington.
On their travels they had contact with more than 360 people.
Today, a third recent case was confirmed - a man in his 60s who flew from Pakistan to Doha and on to Melbourne on June 11, and then to Auckland on Flight NZ124 on June 13 on a Boeing 777-300, which can carry up to 340 people.
A handful of flights are coming into New Zealand each week, carrying Kiwis returning home from Australia and other parts of the world.
The Ministry of Health has also revised its requirements for cabin crew, announcing on Tuesday stricter measures for those travelling as part of their job.
Cabin crew are now required to self-isolate on return to New Zealand and to produce a negative test result before they are able to return back into the community.
Air New Zealand crew doing long-haul flights with a layover also now have stricter requirements, Bloomfield said.
This included stricter requirements for cabin crew flying to the United States, having a layover and returning to New Zealand.
"They now have to self-isolate at home and return a negative test result before they are then allowed to able to go back into the community."
Bloomfield said New Zealand would see more Covi-19 cases at the border because the number of cases worldwide was still growing, and more New Zealanders would be returning so the ministry did expect to see more cases at the border.