Health boss Ashley Bloomfield has defended himself and officials from accusations they have "no heart", following their refusals to grant New Zealanders access to dying family members on compassionate grounds during the Covid crisis.

It comes as New Zealand records zero new cases of Covid-19 but as health officials and the Prime Minister urge caution over whether the country can move down to level 2 as early as Wednesday next week, possibly with a major domestic travel ban eased.

Twenty-four New Zealanders returning from overseas had requested an early exemption from 14-day quarantine so they could visit dying relatives - and the Ministry of Health had refused each one, Bloomfield confirmed today.

"They haven't granted any as at last Friday. The quarantine and self-isolation arrangements... are part of our broader attempts to really get on top of this virus," the director general of health told Newstalk ZB's Mike Hosking.

On Friday, a judge granted Oliver Christiansen the right to see his father after Christiansen rushed home from the UK - and now Prime Minister Jacinda Ardern has ordered a review into the other 23 cases.

Bloomfield told Hosking that significant restrictions had applied to all New Zealanders, not just to people coming in at the borders who had been in self-isolation or quarantined - and the latter were higher risk.

He did not know if any of the 24 had tested positive for Covid-19.

Bloomfield denied Hosking's assertion that the Ministry of Health had no heart and was treating the pandemic as a "medical experiment".

"Far from it... the people who work at the Ministry of Health have a heart for people and they worry about people's wellbeing. They are doing their best to protect all New Zealanders."

Staff got out of bed every day and were working seven days a week to ensure the health of Kiwis, he said.

Covid-19 was not the only focus - the ministry had its eye on many issues including mental health, he said.

Christiansen's father lay dying and asking: "Where is my boy? Where is my boy?"

But up until the judicial decision on Friday, Christiansen couldn't see him - he was subject to the Government's mandatory 14-day isolation period after arriving in New Zealand on April 23 on a flight from the United Kingdom.

Christiansen spoke to the Herald about his "eight days of battling and about 36 hours to spare" before his father Anthony Christiansen, who had brain cancer, died.

Asked by Hosking whether staying in level 3 with zero cases yesterday was "laughable", Bloomfield disagreed. "Many many Kiwis accept that the position we are in now is because we have put in the hard yards - we are not quite there yet."

Meanwhile, Ardern says a day of zero new Covid-19 cases is a national badge of honour - but also warns level 3 will continue as there is no room for complacency.

Ardern is expected to clarify what alert level 2 will look like on Thursday, but stressed Cabinet will need the latest data about Covid cases before it makes a decision next Monday about whether to move down from level 3.

Current guidelines for level 2 advise against any non-essential inter-regional travel, but Ardern said she was open to changing that.

"I know that is incredibly important for domestic tourism. I have heard not only the tourism industry, but also those separated regionally from family and friends - we'll be weighing all those issues up."

She is also dampening expectations that a transtasman Covid-free bubble is close, even though she will today beam in to Australia's national Cabinet meeting via video link.

"Don't expect this to happen in a couple of weeks' time," Ardern said at her post-Cabinet press conference yesterday.

"It will take a bit of time to make sure we can do that safely."

Tourism Industry Aotearoa chief executive Chris Roberts said if the domestic and transtasman tourism markets were opened, it could save several tens of thousands of jobs.

"We would basically have about three-quarters of our tourism industry back," Roberts told the Herald.

He said a recent survey of members found that about 50 per cent of tourism-related jobs were in doubt.

"In a worst-case scenario that is approaching 200,000 job losses, which would be devastating. But we can save some of those by getting a gradual restart of tourism."

Yesterday was the first day in seven weeks when no new coronavirus cases were recorded in New Zealand.

The total number of confirmed or probable cases stood at 1487, but the number of active cases dropped to 191 while the number of people in hospital dropped to four.

"We can take heart in recording no new cases," Ardern said.

"Despite this result my message remains the same: stay the course."

There were 593 level 3 breaches up until Sunday evening, including 154 prosecutions and 400 warnings.

Ardern said having no new cases was down to the success of the level 4 lockdown, and the two-week incubation period of Covid-19 meant that the success of level 3 wouldn't show up in the numbers until later this week.

"I'm a perfectionist. I want to see those numbers after we've been at alert level 3 long enough for it to be a reflection of level 3.

"This is where we check we're recovering well and if we've got it right. We need a few more days to check we have."

Bloomfield said New Zealanders should be proud of what has been achieved, but yesterday's result was "just one moment in time".

"We're nearly there but let's not slacken off now."

He said there were two cases of recent community transmission, and they were both suspected of being linked to overseas travel. Targeted testing around both cases had not revealed any positive tests.

University of Otago epidemiologist Professor Michael Baker said hitting zero was of "huge symbolic value", but he was looking for a sustained trend.

"Everyone in New Zealand should regard that as a positive milestone and reflect on the fact that it is so much better than the alternative we faced six weeks ago, when we were looking at an exponential rise in cases.

"But it is not a guarantee that there is no circulating virus in New Zealand. We will almost certainly get more cases reported later this week.

"It's no basis for relaxing our guard at all."

Baker said more safety measures should be considered before a move to level 2, including a contact-tracing app and a "mass-masking" policy.

"Level 2 is potentially a lot of indoor contact in confined environments - public transport, retail and hospitality, and indoor gatherings up to 100 people.

"That's returning to a high level of social mixing."

But Bloomfield said that having an app up and running was not a prerequisite for moving to level 2 and has previously pointed to World Health Organisation guidelines as a reason for not endorsing mask-wearing in public.

He said easing domestic travel restrictions at level 2 would not make him nervous.

"What would make me nervous is if we were not maintaining those core public health behaviours that we need to maintain, particularly around physical distancing, hygiene and not going out if you have symptoms."