"We are expecting more cases. There is a stronger chance that any new cases will have exposure sites which makes the job of tracing and testing much bigger."
Gunner also announced that Darwin, Palmerston, and Darwin rural areas will enter into a 48-hour lockdown from 1pm today (local time).
"I cannot rule out the lockdown being longer, or expanding the boundaries of the lockdown," he added.
A new Covid-19 case has also been reported in Perth's northern suburbs.
In response to the latest case, which is believed to be part of the Delta variant, a slew of new restrictions has been implemented in the Perth and Peel regions.
Cook said it's believed a woman was infected with the Delta strain while having lunch at the Lyfe Cafe at Bondi. She later returned to Perth on June 20 where she tested positive to the virus.
Despite this, full genomic sequencing has yet to confirm what exact variant of her infection.
Gunner also said that masks must be worn if residents are leaving their place of residence.
"For everyone in the lockdown area, if you leave your place of residence for one of the five reasons you must wear a mask," he said. "Your ordinary place of residence is where you are now."
According to current genomic testing, the NT's chief health officer, Dr Hugh Heggie says the cases are believed to be linked to the highly contagious Delta variant.
"I describe that because our local laboratory which has tested a lot of positive cases can detect a shadow of the Delta virus," he said.
"This is critical for our community that we do not see further spread within the community."
Heggie also said that there is no current threat to any remote communities, however, this could change.
"There is no current implication for remote communities, apart from these mine site but this is an absolutely evolving situation and that information will be updated as we learn more," he said.
"Please, please, be patient, look after yourselves and obey the rules."
In relation to the 48-hour lockdown Gunner said that he hopes this period will allow authorities to analyse test results and establish the next steps.
"It is based around the testing cycle," he said.
"It might be that once we get through the 48 hours we may need to extend for longer.
"We are confident that the 48 hours allows us the time to do the work and allows us the time to get a greater degree of information about lifting or extending."
When asked whether there was any "frustration" over the fact that initial NT case was linked to a Queensland quarantine hotel, Gunner said he had "no aspersions on other states".
"I think we are all extremely mindful of the pressure every state has been under for 18 months," he said.
"We understand the limitations of hotel quarantine. I have sympathy for other states.
"I'm not here to criticise the Government. This happened and we're dealing with it."
Darwin's snap lockdown comes one day after Sydney entered a two-week lockdown after Covid-19 cases grew in the city.
Residents will only be able to leave the home for four essential reasons. They are:
1. For medical treatment
2. To purchase essential goods and services
3. For essential work
4. For one hour of exercise a day with one other person or the people you live with.
