The 31-year-old man, 82-year-old woman and two children, both aged three, were passengers on a Commonwealth repatriation flight that arrived from India on Tuesday.

NT Health said on Thursday all four were in isolation at the Howard Springs camp under the care of medical staff and remained well.

The total number of active cases in the NT is now five.

It follows the diagnosis of a 31-year-old woman on Wednesday, who was on the same flight from New Delhi.

She tested negative for the virus before travelling but positive at the repurposed mining camp on Darwin's outskirts.

NT Health said returned overseas travellers were a high-risk group and five to 10 per cent could test positive for the virus.

This brings the total number of cases diagnosed in the NT to 39. All infections are related to travellers coming into the territory and not community transmission.

The new cases come as NT police fine two people at the Howard Springs facility for breaching quarantine rules.

A woman, 33, was fined after allegedly attempting to climb over the perimeter fence at the camp.

A man, 57, was fined after he was allegedly found outside his unit while not wearing a mask.

When questioned by staff the man allegedly became aggressive.

The penalty for failing to abide by the chief health officer directions is $5056 for an individual and $25,280 for a business.

Australian Associated Press