The territory government will also ramp up its vaccination program this week, with 24,000 Pfizer jabs expected to be delivered.

Chief Minister Andrew Barr said he hoped to have 50 per cent of population over 16 vaccinated by the end of the week.

The ACT recorded 11 new cases in 24 hours to 8pm on Sunday. Nine of the cases were linked to known outbreaks or clusters but only three were in quarantine for their entire infectious period.

Authorities again expressed alarm about people waiting to get tested after developing symptoms. There is also concern that people are not isolating when waiting for their test result.

Health Minister Rachel Stephen-Smith said there had been reports that people had attended medical appointments while waiting for their COVID-19 test result.

ACT deputy chief health officer Dr Vanessa Johnston said some of the people who had been infectious in the community had stopped for takeaway or groceries on the way or way home from being tested.

"You may think that a quick trip through a drive-through or a quick stop off at Woolworths with a mask is without risk but that's not the case, it comes with risk," she said.

There were 1281 COVID-19 cases reported in NSW on Monday, as that state's outbreak moved further south with several cases reported in southern NSW.

READ MORE:

NSW Deputy Premier John Barilaro reported three cases in Queanbeyan, two cases in Goulburn, one case in Cooma, one case in Batemans Bay and eight cases in the Shoalhaven local government area.

Mr Barilaro said on social media two Queanbeyan cases were believed to be linked to the Canberra outbreak. The third case, from Googong, was a close contact of a case reported last week.

Dr Johnston earlier refused to confirm whether the Queanbeyan cases had been linked to the ACT, saying it wasn't "particularly helpful" to confirm if cases in NSW were linked to the ACT.

It came after the ACT's chief health officer, Dr Kerryn Coleman, confirmed on Sunday that genomic sequencing had indicated there had been multiple introductions of the virus from NSW.

About 95 per cent of cases are linked to clusters identified in the initial stages of Canberra's outbreak. Dr Coleman said that indicated there are a small number of cases coming into the territory from NSW.

An ACT Health spokeswoman confirmed on Monday that investigations had identified four separate genomic links of the virus, this was in addition to that of the initial cluster.

"We are still investigating these cases, including their infectious periods in the community and the nature of their travel to the ACT, however, three of the four have been genomically linked to cases in the NSW outbreak," the spokeswoman said.

"While there is one case we don't have a confirmed genomic link for, we believe it is also connected to the broader NSW outbreak.

"The most recent outside introduction of COVID-19 to the ACT was notified as a case on 1 September."

READ MORE COVID-19 NEWS:

Mr Barr said the ACT's ability to ease restrictions was largely dependent on what happened in NSW. He said vaccination numbers in that state also had a bearing on the territory.

"We need to think about what our public health settings are around controlling the outbreaks that have come into the territory from NSW, but we're going to face the ongoing risk of that for many months," Mr Barr said.

"The risk doesn't go away, it's there every single day until we get our vaccination rates up to the highest possible level and similarly NSW does the same.

"We will always be at risk in this period from NSW, but it's not just about NSW, it's also about internally within the ACT and Canberrans going into NSW can bring the virus back with them as well."

Figures from the Department of Health on Monday showed 69.4 per cent of the ACT's population aged above 16 had received one dose of the vaccine, and 46.3 per cent were fully vaccinated.

However, Mr Barr said the ACT had already passed the 70 per cent milestone, owing to a lag of about 1.5 days between ACT and federal government figures.

When people aged between 12 to 15 are considered as part of the vaccination statistics in the ACT, it's 66.9 per cent for the first dose and 44.5 per cent are fully vaccinated.

In NSW, 74.1 per cent of the population above 16 has received one dose and 41 per cent are fully vaccinated.

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: