The new case takes the territory's total in the current outbreak to seven, with the ACT in lockdown until at least Thursday.

Chief Minister Andrew Barr said there were more than 4500 tests on Friday, "a record day of testing in the ACT".

He said hundreds of tests had already been completed on Saturday, but acknowledged there were "significant delays" at testing sites.

Meanwhile, health authorities remain baffled about how a Canberra high school student with no known travel outside the ACT or link to exposure sites tested positive to COVID-19.

Urgent genomic testing is under way in relation to the 14-year-old from Gold Creek School in the city's north, who had been infectious at school from Monday to Wednesday.

All students and teachers at the school are being treated as close contacts.

Students and staff at the Holy Spirit Catholic Primary School are being considered casual contacts, as they share some services and facilities with the neighbouring school.

On Friday, Mr Barr said the territory would need to record no local cases before an end to the lockdown could be announced.

"The most important thing is what we can do ... over the weekend to ensure that we get to the close contacts, get them in isolation so that they are not a risk to people in the community," he said.

Faced with overwhelming demand for testing, the ACT government is bolstering staff at existing centres and opening sites at Gold Creek and Brindabella.

It is also seeking to reduce demand by asking Canberrans not to get tested unless they have symptoms or have been identified as a close contact by ACT Health.

Federal support has been made available to workers who lose hours and businesses forced to temporarily close.

The ACT's first local case in 13 months was confirmed on Thursday, a man in his 20s with the Delta strain.

Australian Associated Press