Currently, fully vaccinated international travellers are permitted to "home quarantine" in the NT for seven days as long as they submit to mandatory testing.

The Aboriginal Medical Services Alliance Northern Territory says that should be paused to protect the territory's vulnerable Aboriginal population now Omicron has arrived.

"The NT should be cautious until we know more about this new variant," chief executive John Paterson told AAP on Tuesday.

Mr Paterson said unsupervised quarantine in high-density settings, such as hotels and high-rise apartments, could lead to the virus spreading to other residents.

He urged the NT government to resume supervised quarantine for all international arrivals at a facility, such as The Centre for National Resilience, south of Darwin.

"At the very least, hotels and multistorey apartments should be removed as an option for home quarantine," he said.

Australia's third Omicron infection was confirmed in the Howard Springs quarantine facility on Monday after a man in his 30s was diagnosed with the virus.

He arrived in Darwin on a repatriation flight from South Africa on Thursday and his positive virus result was confirmed on Friday.

Currently, international arrivals on repatriation flights are required to quarantine for 14 days at Howard Springs.

Travellers who arrive on the daily standard international flights into Darwin Airport are permitted to quarantine for seven days at their homes or another suitable location.

The flights are expected to become twice daily from December 19.

The home quarantine requirement is scheduled to end on December 20 but all arrivals will be required to have a rapid antigen test.

Meanwhile, the NT detected no new COVID-19 infections on Tuesday.

The current outbreak remains at 58 cases.

"That's really good news," Health Minister Natasha Fyles said.

"Importantly, some of the key indicators we have been using have also given us some positive results today."

Wastewater testing returned negative results in Katherine, 320km south of Darwin.

Vaccination rates continue to climb in the town, with Ms Fyles saying it's almost reached 80 per cent double dosed.

A lockout in Katherine and its surrounding area of unvaccinated people will remain in place until December 7.

Wastewater testing in the remote Aboriginal community of Lajamanu, 900km south of Darwin, has returned a weak positive result.

The community of about 1000 was put into lockdown on Saturday after the virus was detected in wastewater samples.

But Ms Fyles said this may have come from a traveller and not a resident, and health workers continue to test the community for the virus. No cases have been identified.

Binjari Aboriginal community, 330km south of Darwin, remains in a hard lockdown with residents only permitted to leave their homes in an emergency or for medical treatment.

Testing also continues in the community of about 200 people, with Ms Fyles saying restrictions may be eased if no new cases are detected.

Robinson River also remains locked down as testing continues.

Australian Associated Press