The new cases include four men and one woman, aged between 27 and 73.

Of the new cases, four are linked to overseas travel and one is a close contact of a confirmed case.

Of the 44 cases, 14 were acquired on cruise ships.

There have been 2964 negative COVID-19 tests in the ACT to date.

There are currently three COVID-19 patients in Canberra Hospital while the rest are self-isolating.

There are a further 480 Canberrans in self-isolation and quarantine after initial testing.

Health authorities said there were 27 international flights that coronavirus cases in Canberra travelled in on, some arriving as recently as Sunday.

Mr Barr said Canberrans needed to be there for one another, warning restrictions would get tougher.

"We are physically distant but we should not be emotionally distant from each other," he said.

"As the Prime Minister said this is probably going to be the most difficult year in people's lives.

"We recognise that the economic impact this is having will be deep, and governments right across the country are working together to respond to respond to the circumstances as best we can."

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ACT chief health officer Kerryn Coleman said there was still no evidence of community transmission in Canberra

"ACT health are working very hard to make contact with close contacts of confirmed cases as a priority," she said.

Dr Coleman said ACT Health was considering real-time tracking of the number of confirmed coronavirus cases, after Victoria introduced the initiative on Wednesday.

Mr Barr said he wanted to avoid situations seen in Europe where ice rinks were being used as temporary morgues following a surge in deaths from the virus.

He said relaxing more lockdown restrictions in a matter of weeks would lead to authorities playing "whack-a-mole" with new virus cases until a vaccine is found.

"Doing that for the next 12 months is a difficult task, its a huge ask for the community," Mr Barr said.

"There's the idea that having a shutdown for two, four or eight weeks would solve the problem. It doesn't.

"As soon as you unlock, [virus cases] start again, and I don't think enough people understand that."

Health authorities said those who had been diagnosed with the virus and weren't in hospital were complying with self-isolation measures.

Mr Barr said he would take further advice on calls to use mobile phone data to track movements of those in self-isolation to ensure they don't spread the virus throughout the community.

As Victoria moves to implement further restrictions, Mr Barr said the ACT would look to be consistent with measures seen in NSW.

"We'll work through the national cabinet and adopting a Canberra-region approach, but looking at the circumstances, it's clear jurisdictions may need to adopt more significant measures earlier than others," he said.

"In that case, we're likely to move earlier."

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