Prime Minister Jacinda Ardern wants Covid-response workers to avoid face-to-face meetings with border-facing workers to minimise the risk of catching the virus.
And they should avoid traveling for such meetings, she says, and wear a mask on planes if they have to travel.
But she is stopping short of making mask-wearing mandatory on planes and public transport at alert level 1.
The moves follow at least seven instances in just over three months where Covid-19 has been transmitted from within a managed isolation or quarantine (MIQ) facility into the community.
The latest case is a Defence Force worker who caught Covid-19 while working at the Jet Park quarantine facility in Auckland, and then infected a Defence Force civilian worker at a meeting on Wednesday.
"Having an individual travel in for a meeting with MIQ workers represents a risk that could be avoided," Ardern said.
"Using remote ways of meeting and reducing down travel of those in contact with MIQ workers are all things [Covid 19 Response Minister Chris Hipkins] will be seeking assurances from the Defence Force around."
Asked if it would change immediately, Ardern said: "Yes, I imagine so."
The civilian worker, who didn't have symptoms at the time, then took a flight from Auckland to Wellington on Thursday - but didn't wear a mask.
"If there is travel in a circumstance like that, there would be an expectation of mask use," Ardern said, adding that she was not blaming anyone.
"That is something we will be requiring."
While none of the nine people sitting within two seats of the worker on the plane have tested positive so far, another traveller on the plane became unwell and was tested for Covid-19.
Communities in the Waikato were on high alert yesterday after learning that the person had traveled there, and were later relieved last night to be told they had tested negative.
The Health Ministry is also looking at whether N95 masks should be worn by healthcare workers who work in quarantine settings.
N95 masks protect against contagious air particles, and director general of health Dr Ashley Bloomfield said they were better at preventing infection than the surgical masks which are currently used.
"If there is a higher risk of aerolised virus, that may mean those workers having more regular interaction with people who are known to be infected should be using N95 masks."
Bloomfield said the latest cases appeared to be well contained and there was no reason to change alert levels at this stage.
There were four new cases of Covid-19 yesterday - all imported cases in managed isolation facilities and no more community cases.
Bloomfield said there was a case for compulsory mask-wearing on flights and public transport, even though the Government decided against it for level 1.
Public health expert Dr Amanda Kvalsvig said Kiwis deserved to know why.
"It is hard to see why the Government has held back from taking this potentially life-saving prevention measure."
Asked about this last week, Hipkins said public compliance remained a crucial factor in the ongoing Covid war.
Ardern added that there could be knock-on effects.
"It means that someone would not be able, for instance, in Invercargill to access public transport if they did not have a mask.
"I wear a mask on a plane. I encourage others to wear masks on a plane. I encourage people to use them on buses. In places where you have close contact with people you don't know, I would absolutely in those environments encourage mask use."
She said Government officials will head to the Cook Islands on Saturday to see if the practices put in place were safe enough to open a quarantine-free travel bubble.
Talks were also continuing with Australia, but Ardern said they needed to agree what qualified as a hotspot in Australia, which would trigger a travel ban.
A hotspot had previously been defined as more than 10 cases per day over a three-day period, which Ardern said was too risky.
When it is safe enough to open a trans-Tasman bubble, it is expected to clear 40 per cent of the rooms in MIQ facilities.
Yesterday, following lower-than-expected demand, the Government has made about 100 rooms a day available again from December 13 to 23.
Meanwhile Bloomfield praised a person for seeking clarity after sitting in the same row as the infected Defence Force worker on his flight to Wellington.
Kiwiblogger David Farrar said he had been contacted by the person's family, who were frustrated at being told six different types of health advice from the Health Ministry, Healthline, and a public health unit about whether they needed to isolate.
"There was conflicting advice and this person did exactly the right thing and clarified that advice," Bloomfield said.