The blunt remarks came as Chief Police Officer Neil Gaughan warned that anyone who posted recriminations and comments on social media against the man could be in breach of federal laws.

Mr Barr on Friday again refused to be drawn on how the Gunghalin man in his 20s caught the virus, declining to confirm or deny speculation that he had become infected after travelling to Sydney.

"We will address those sorts of issues later," Mr Barr told Friday's media conference.

"That is entirely unimportant at the moment because it will do absolutely nothing to address the situation that we face today, which is about identifying close contacts, testing people that we need to get tested and advising of the exposure sites.

"There is a time for those issues, but not today."

Asked if ACT authorities were any closer to establishing the source of the man's infection, and whether it might have involved a breach of public health rules, Mr Barr said: "We are still working through the details there".

The man is reported on social media to be a nightclub bouncer who left the Fiction Bar in Bunda Street at 4.45am on Sunday morning, August 8.

QR code check-in tracing then showed he checked in at the Pentecostal church in Irving Street, Woden, at 10.30am for a two-and-a-half-hour session, before visiting Freedom Furniture, TK Maxx and Windsor Smith shoes store at the Canberra Outlet Centre in Fyshwick between 2pm and 3.25pm.

READ MORE:

The mystery case had led to four further infections as of 9am on Friday, all close contacts.

Chief Police Officer Gaughan indicated on Friday that police were looking into the man's circumstances.

He also warned social media users of the potential consequences of posting about the man online.

"I see there is a lot of [social media] focus on one individual, I think that's really dangerous," he said.

"It's not a kangaroo court.

"There are a lot of offences under Commonwealth legislation as to naming people on social media so I ask people to be very cautious about what they are posting.

A second unlinked case was announced on Friday morning - a 14-year-old student at Gold Creek school, who hadn't travelled outside the ACT or visited one of the listed exposure sites.

Our coverage of the health and safety aspects of this outbreak of COVID-19 in the ACT and the lockdown is free for anyone to access. However, we depend on subscription revenue to support our journalism. If you are able, please subscribe here. If you are already a subscriber, thank you for your support. You can also sign up for our newsletters for regular updates.

Our journalists work hard to provide local, up-to-date news to the community. This is how you can continue to access our trusted content: