Australia's acting chief medical officer Professor Michael Kidd made the announcement at a press conference today.
He said Australia's health authorities had been advised by New Zealand that the three Covid-19 cases were genomically-linked and had the "variant of concern".
"The HPPC [Health Protection Principal Committee] has recommended that the commonwealth extends the pause in safe travel zone flights from New Zealand for a further 72 hours.
"This recommendation has been made to the Australian Government, the Australian Government has accepted the advice, so the travel pause on green zone [flights] from New Zealand to Australia has been extended a further 72 hours.
"The allows continuing protection of the people of Australia while the extent of the situation in New Zealand is clarified," he said.
"I apologise to those people who've had their travel arrangements disrupted."
On January 25, Australia's Health Minister Greg Hunt announced the country would suspend the travel bubble for at least 72 hours out of an "abundance of caution" following the discovery of the South African Covid-19 variant in the community.
The changes came into effect on Monday at 2pm Australian time and arrivals to Australia from New Zealand are now required to enter a 14-day quarantine.
At the time, Kidd said the government would wait on further information before deciding whether to extend the suspension.
"The situation is evolving rapidly. We will be following up the details of both of these cases with the New Zealand authorities once further details, including the results of additional testing, are known," he said on Wednesday.
"We need to wait until we hear further details from our colleagues in New Zealand about further tests which are being carried out.
"We do expect that it is likely that both of these people would have had tests carried out during their 14 days in quarantine, but again we need to wait and get those results."
Meanwhile, Australia has confirmed 10 days without a case of community transmission. The country's longest stretch without a community transmission infection was 12 days in December.