While earlier on Thursday eight Territorians were reported as having tested positive for COVID-19, all of whom were in hospital in Darwin, the number of positive cases stands at a dozen, according to figures published on the NT government's website.

A couple from Katherine and a couple from Central Australia who had returned from overseas returned positive tests on Thursday, the NT News reported.

It comes as the current NT school term is set to finish a week early in response to the coronavirus pandemic.

The final four days of this school term - April 6 to 9 - will now be professional development days for staff to prepare for the continued delivery of education in term two, the NT government said in a statement.

Students will not be required to attend those days, but schools will remain open and no child will be turned away - including the children of workers who cannot make alternative arrangements, and vulnerable children.

School will continue as usual next week but parents and families can choose to keep their children home if they wish, the statement said.

NT Health Minister Natasha Fyles said the government wants to make sure children still have access to education.

"If we take our kids out of school for a couple of months in grade one or two they can't make that up very easily," she told reporters.

It is unclear whether term two will take place in the classroom or at home.

A Darwin couple aged in their 70s who on Monday returned from New York tested positive for the virus on Thursday.

They had followed self-quarantine protocols on their return to Darwin, Ms Fyles said.

She said there had been no community transmission of the virus in the NT yet.

Strict new measures introduced this week have included border controls requiring new arrivals in the NT to self-isolate for 14 days, while airlines Jetstar and Virgin have stopped all services to Darwin.

Northern Territory Correctional Services has stopped all social visits to prisoners and ceased prisoner work party camps in the community.

New restrictions on remote indigenous communities are in place, with all potential visitors now required to quarantine themselves for 14 days due to Aboriginal people being regarded as more vulnerable to COVID-19.

All national parks including Kakadu and Uluru in the NT have been closed from Thursday night to discourage unnecessary travel.

Australian Associated Press