The ACT reported 20 new cases of COVID-19 in the 24 hours to 8pm on Tuesday, including seven people who had been in the community for at least part of their infectious period.
Nine of the new cases have been linked to known cases or outbreaks, but 11 of the cases are still under investigation.
There are now 10 people in hospital, with two people being treated in intensive care. One person requires ventilation.
Mr Barr again stressed the the next few months in Canberra would be difficult, as restrictions could only be eased when the health risk of a virus outbreak fell.
"Our primary goal remains the health and protecting the health of our community. We are very acutely aware of the need to consider the economic impacts, and the mental health and wellbeing impacts of public health restrictions," Mr Barr said.
"To be as blunt as I can be, if the virus gets out of control in Canberra, we will experience even greater health and economic challenges than we are now. We can't let that happen - and we won't."
Mr Barr said he had not given up hope of so-called COVID zero days, but the next phase for the ACT would be to move from high public health restrictions to medium level restrictions.
"I'm not going to give up on the suite of public health measures that bend the curve, but it's clear that we're not going to have double zero days tomorrow or the next day," he said.
"We're going to have to continue to vaccinate, we're going to have to continue our effective test trace isolate quarantine scheme."
Mr Barr said the test, trace, isolate and quarantine scheme, had been effective but not perfect.
"Any movement is going to be gradual," he said.
There were about 3400 COVID-19 tests conducted on Tuesday, and Chief Minister Andrew Barr said this was a good level of surveillance.
The ACT set a record for vaccinations on Tuesday, with 4737 doses administered.
More than 80 per cent of the ACT's over-70s are vaccinated, which Mr Barr said he believed was an Australian first.
There have been 424 cases of COVID-19 identified in the ACT since the start of the outbreak, including 193 people who have recovered from the virus. There are 231 active cases.
Deputy chief health officer Dr Vanessa Johnston said 34 people had been hospitalised throughout the outbreak, including six people who received treatment in intensive care.
ACT Health was working with 1500 self-identified close contacts across 350 active exposure locations, Dr Johnston said.
Professor Catherine Bennett, who holds the chair in epidemiology at Deakin University, said the ACT does not need to eliminate the COVID-19 virus from the community to successfully contain the current outbreak, given the growing rate of vaccination.
"At the end of the day, it is about vaccination ... It doesn't mean you can't go to COVID-zero, it just means you don't need to put all your controls in place as if you need to get back to COVID-zero," she said.
Professor Bennett said more extreme public health restrictions could be eased if the number of cases in the ACT was being kept to a minimum, after vaccination targets were reached.
Meanwhile, exposure site locations continue to be identified in suburbs across Canberra, including an O'Connor chemist on multiple days.
Capital Chemist O'Connor was an exposure site on Wednesday between 3.40pm and 4.20pm, Friday between 10.50am and 11.30am and Saturday between 2pm and 2.40pm.
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Anyone who visited at these times should monitor for symptoms and get tested immediately if they develop.
Supermarkets in Amaroo, Narrabundah, Ngunnawal, Holt, Mawson and Lyneham, as well as bottleshops in Gungahlin and Mawson are also among the recent "monitor for symptoms" sites.
On Tuesday, a number of restaurants offering takeaway in Belconnen were added to the monitor list.
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