Four of the new cases are linked to the current community outbreak, bringing the cluster to 144 cases.
Two are people from the Tennant Creek area and two from the Katherine area, NT Health said on Sunday.
All are in isolation and contact tracing is underway.
Two new locally-acquired cases linked to an infected interstate traveller were diagnosed in an NT household.
Six other interstate arrivals also tested positive.
They are all in isolation at their homes or at The Centre for National Resilience in Howard Springs, near Darwin.
There are currently 18 people with COVID-19 in NT hospitals, including one in person in intensive care.
The community outbreak started when an infected woman illegally entered the territory in late October.
The 21-year-old was fined for lying on her border entry form as the virus spread from Darwin to Katherine, 320km south of the territory capital, and multiple Aboriginal communities.
Police have since launched a fresh investigation into the border breach after an Aboriginal woman died from COVID-19 in early December.
Meanwhile, children aged five to 11 can now roll up their sleeves for the jab in the NT, with online bookings open.
The paediatric Pfizer COVID-19 vaccine will be available from January 10.
To be fully vaccinated, children will need to receive two doses eight weeks apart.
The dose is one third of the amount compared to the vaccine for people aged 12 and over.
More than 95 per cent of Territorians aged 16 years and over have received two doses of the COVID-19 vaccine.
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