Victoria Premier Daniel Andrews has indicated the changes would be more "in the social space", prompting pleas from business operators for relief from restrictions that once included an overnight curfew.
In a press conference today, Andrews said Victoria authorities had been alerted to the increased number of breaches by Australia's federal government.
"To say that people were quite surprised that we found ourselves in this bubble despite the fact we had said we would not be, would be an understatement". "So this is the gold standard, apparently, according to the federal government", he told reporters.
"One of them was in Byron Bay [in New South Wales] and yet we were told they had landed and travelled to Melbourne".
New Zealanders arrive at Sydney Airport.
"We can not just have people wandering into the place from another country".
They also extended from five to 25 kilometres the distance people could travel from their homes for several activities, including exercise, shopping for essentials, socializing and work in essential professions.
Good news for Victorians in need of a haircut - from 11.59pm tonight, hairdressers can reopen as restrictions ease in Victoria.
And Western Australia Premier Mark McGowan has confirmed 25 people - including a child - from New Zealand are now in hotel quarantine, after flying into Perth overnight.
Yesterday, Andrews said he was "very disappointed" 17 travellers from New Zealand were able to enter Victoria, despite the state not taking part in the travel bubble that started on Friday.
Andrews said there were now authorised officers based at Melbourne Airport as a result of the incident.
"We didn't think it would happen, but it has happened".
The global border remains closed to non-residents, other than a limited travel bubble with New Zealand, and those returning from overseas must undergo 14 days of quarantine in hotels or other government-run facilities.
Mr Tudge said the Victorian Chief Health Officer, Brett Sutton, was present at meetings about the New Zealand travel arrangements earlier this week, and no objections were raised. They are all in quarantine.
Passengers from New Zealand would not be deported, he said.
Prime Minister Scott Morrison welcomed the decision to loosen the strict controls but sympathised with businesses' "frustration and concern".
He said his office still was not able to obtain travel cards from the Australian Border Force as to "who these people are and where they have gone". "We are going to follow up as much as we can". "We made it clear that we didn't want to be part - could not be part of the bubble arrangements at this point".