Authorities are still trying to find out how two people in Canberra got coronavirus, but say it is too early to determine if it was community transmission.
ACT Chief Minister Andrew Barr on Monday said they were trying to find out if they were the first cases of community transmission in the territory.
"They are still undertaking that work. There isn't new information as at 8.30 but I understand there will be in the not too distant future," he said.
"And if we can contact trace and identify the source, then they will fall into one of the existing categories .... or if there isn't a clear link to any of those then we may indeed have our first unexplained, and therefore quite potentially community transmission cases."
Six new cases of coronavirus were confirmed in the ACT on Sunday, bringing the territory's total to 77 cases. The new cases were four men and two women, aged between 19 and 82.
Three of the new cases are linked to overseas travel, two are close contacts of confirmed cases and one is under investigation by Health Protection Services. There is no evidence of local transmission, ACT health says.
Authorities were also trying to determine how a case announced on Saturday contracted the virus.
ACT Health Minister Rachel Stephen-Smith said neither of the two were Canberra health workers. The government had said health workers contracting the virus would be a clear sign of community transmission in the ACT.
"Investigating [the source of transmission] can be quite complicated and we're talking to interstate colleagues as well to where [the patients'] exposure points have been and whether it's been a flight or other location in other jurisdictions," Ms Stephen-Smith said.
"There's also a lot of modelling going on at the national level and that conversation is going on.
"What we have to understand is that health systems around the world are different and people are seeing growth of the virus being different in different countries."
Ms Stephen-Smith told the media on Sunday that while the ACT had no recorded cases of community transmission of the virus, it would be inevitable that it would occur.
"At some point, probably in the next week, we will have a case of community transmission in the ACT, and that will be another wake up call for Canberrans and we absolutely need to be 100 per cent vigilant in social-distancing measures," Ms Stephen-Smith said.
There have been 4230 negative COVID-19 test in the ACT so far.
Six patients remain in Canberra hospitals while the others are isolating at home with support from ACT Health.
Two of the patients in Canberra Hospital are in intensive care.
Two cases have recovered and been released from self-isolation.
The Health Minister said work was under way in determining how many bed spaces Canberra's private hospitals would be able to hold should other patients need to be transferred to free up wards.
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