Ashley Bloomfield, New Zealand's director-general of health, said there was an "agreed plan in place" to let the two women from the United Kingdom enter New Zealand to see their dying relative, the BBC reported.
New Zealand had lifted all social and economic restrictions except border controls last week, after declaring it had no new or active cases of the coronavirus, one of the first countries in the world to return to pre-pandemic normality.
Before the two new cases were announced Tuesday, New Zealand had gone more than three weeks without reporting any new cases and was considered virus-free.
They were granted permission to journey to Wellington on 13 June.
"I apologise that we've ended up in this position", Bloomfield said.
They were released from quarantine early, despite one showing mild symptoms of the virus. They must be disciplined, and they must have the confidence of ministers and all of you - New Zealanders - who got us here.
The women were carrying a "supply of face masks" with them but were not tested before they left the Auckland hotel.
The new cases followed 24 consecutive days of no new cases in the country.
Consumer inflation continues to ease in May
That was largely due to slowing food prices, which rose 10.6% in May from a year earlier, versus a 14.8% rise in April. Energy prices continued to fall in May, dropping 1.8 percent on the month, and 18.9 percent year-on-year.
It was revealed on Tuesday that two sisters who later tested positive for the virus were allowed to leave managed isolation in Auckland to travel to Wellington after their mother had died.
New Zealand is seen as having led the way in its response to the COVID-19 outbreak. Questions are now being raised about the Health Ministry's insistence that the women had no contact with anyone on the road trip - a distance of more than 600 kilometers (375 miles) that would take at least eight hours. However, due to the current restrictions in place requiring all inbound travellers to quarantine, they were staying in a "managed isolation hotel".
New Zealand has recorded 1,506 confirmed and probable cases of COVID-19, and 22 deaths.
ASHLEY BLOOMFIELD: We have had two cases.
In addition, health authorities have been informed of instances where friends have made contactless deliveries of food or care packages to the women while they have been in self-isolation in recent days.
Both are self-isolating now.
Prime Minister Jacinda Ardern said this case proved the need of a rigorous system at the border and appointed a military leader to oversee quarantine and managed isolation facilities.
More than 300 people are now set to undergo Covid-19 tests after the news came to light, while gaping holes seemed to be exposed in the border procedures so critical to our strategy of elimination.