According to Mr Barr all three cases come from the same household and are all linked to the outbreak in Victoria.

"We recognise this is hard news, Canberrians did not want this outcome, the Government did not want this outcome, no one wanted this outcome," Mr Barr said on Wednesday.

"We have done a lot of work as a community to suppress the virus, but as we have stressed before the virus is not eliminated in Australia and it is certainly not eliminated around the world so it was highly likely that there would be new cases here in the ACT as there will be in other states and territories."

According to Mr Barr the outbreak in Victoria has reinforced and confirmed absolutely that the pandemic is a long way from over.

"We need to remain vigilant and maintain all of the practices that we've been undertaking since the pandemic commenced," he said.

Mr Barr stressed the importance of Social Distancing, personal hygiene and listening to the directives from state and Federal authorities and went on to state emphatically that anyone wishing to enter the ACT from Victoria will require an exemption.

"ACT residents will of course be able to return home but they are required, absolutely required to notify ACT Health so that we know who they are, how they are planning to return to the ACT and what their 14 day quarantine plan is," Mr Barr said.

"We continue to watch what is happening in Melbourne and the return to the lockdown measures that the Victorian Government has announced.

"We know that is going to be incredibly difficult for millions of Melburnians and certainly no one wants that to occur in Canberra and that's why we are asking all Canberrians and visitors, anyone who has been in Victoria in recent days and weeks to be careful, incredibly careful act like you have the virus."

Mr Barr stressed that anyone who was showing signs of any of the symptoms of COVID-19 should be tested as soon as possible.

Mr Barr said the ACT Government would make a decision in regards to the further easing of restrictions in the Territory towards the end of the week.

On Wednesday NSW Premier Gladys Berejiklian warned of tougher action being taken if residents in southern NSW continued to move around from or to the border region, including the suggestion of a 'border bubble' north of Albury.

"I do want to send a very strong warning the probability of contagion in NSW given what's happening in Victoria is extremely high," Premier Berejiklian said.

"The probability that we need to be tougher on those border restrictions is extremely high."

Ms Berejiklian stressed that residents in the border region not travel outside of their towns.

"I ask everybody in those border communities including residents in NSW that live in Albury or Moama or other places across the border do not travel to other parts of NSW unless you absolutely have to," Premier Berejiklian said.

"If you are an Albury resident we do not recommend you travelling to other parts of NSW and if we feel in the next few days or as early as tomorrow (Thursday) that we need to further protect the community we will consider what we do north of Albury.

Ms Berejiklian said though she understands the tougher restrictions could be an imposition not only on border residents but those across NSW the Government will not flinch in tightening restrictions if needed.

"We can certainly control what happens on our side of the border but we can't control what's happened on the other side of the border," Ms Berejiklian said.

"I've already had advice this morning (Wednesday) that there's at least one person from Wodonga who has the virus we're still awaiting details."

Ms Berejiklian said even the permit process is filled with risks.

"When you have communities mixing with each other crossing a border it carries enormous risk," she said.

"So I will stress the Government is considering what further action we take to make sure the bubble as we call it of those border communities is maintained.

"For communities like Wagga Wagga and others who have close interaction with people in Albury I ask you not to visit those border communities from other parts of NSW unless you absolutely have to and similarly we say to NSW residents who live in those border communities do not move outside your border community unless it is absolutely necessary otherwise we will need to take further action which could further compromise your ability to move freely.

After almost two months of no positive COVID-19 cases in the Murrumbidgee Local Health District there were two confirmed cases in the region on Monday evening.

The announcement came on the same day the NSW and Victorian Governments announced a hard border closure between the states.

According to NSW Health on Monday the two suspected cases returned preliminary positive results for the virus and authorities were investigating the cases for contact tracing with close contacts identified and put into self-isolation.

"We've had some new cases arise near the border area in the Lovington/Albury region," Murrumbidgee Local Health District's Infectious Disease Specialist Dr Timothy Gibley said on Tuesday.

"We've had two confirmed cases which have been traced and confirmed to have direct contact with known hotspots.

"The source is clear which is always reassuring.

"At the moment we are following those cases in terms of the contact tracing and there's been isolation instigated to keep those under taps."

According to Dr Gibley the two positive patients had not travelled through the region much before they presented for testing.

"There wasn't a great deal of exposure (from the positive cases), there was some travel through the area over a 24 to 48 hour period only and not a lot of particular contact," Dr Gibley said.

"It speaks to the need to be vigilant."

Murrumbidgee Local Health District is urging any locals who may have been in the area over the past week who have developed even the mildest of symptoms to please get tested as soon as possible.

In the 24 hours up until 8am on Wednesday morning MLHD reported their were no further cases recorded.

In response to the positive tests and the number of people who have come forward for testing in Albury, MLHD announced on Tuesday afternoon they would be sending further health workers to help.

"MLHD is sending additional nurses and extending the hours of the pop up clinic in Albury after a higher than expected turn out of local residents," an MLHD spokesperson said.