Western Australia's borders will remain closed but other restrictions could be unwound within weeks as the number of new coronavirus cases continues to fall.
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Just one local case was recorded overnight, while three foreigners onboard the plagued Artania cruise ship also tested positive.
The four new cases took the state's total to 527, including 296 people who have recovered and 32 currently in hospital.
More than 200 confirmed cases have been linked to cruise ships, including 75 from the Artania and 54 from the Ruby Princess.
Hard border closures and intrastate travel bans have helped keep community transmission low.
Premier Mark McGowan says other restrictions might be rolled back next month.
"We're going to work on this over coming weeks to see what can be eased and can be tweaked, but I don't want to start ruling things in or out now," he told reporters on Tuesday.
"The restriction I'm not going to let up on, certainly in the near to medium term, is the interstate border."
Almost 37,000 people were stopped at regional border checkpoints during the Easter weekend, with 876 denied entry.
Three people received on-the-spot fines for breaching physical distancing requirements, while traffic on major roads was down about 90 per cent compared to last year.
"People listened to the advice, followed the rules and we all got the outcome we were hoping for," Mr McGowan said.
The premier said he was confident the Artania and its roughly 400 remaining crew would leave Fremantle over the weekend.
The government is considering options for repatriating people from other states who are stuck in Perth, as well as bringing home West Australians stranded interstate.
Passengers could be moved on chartered flights or via train on the Indian Pacific.
New residential tenancy laws will also be introduced to parliament which ban evictions for six months, except for in limited circumstances, and freeze rent increases.
At least 2000 health workers will help test whether an existing tuberculosis vaccine could reduce the chance of COVID-19 infection and lessen the severity of symptoms.
Andrew Forrest's Minderoo Foundation has committed $1.5 million to support the rollout of the BRACE trial using the Bacillus Calmette-Guerin vaccine.
The state government will also spend $400,000 to provide a free influenza vaccine for primary school aged children.
"We've had a tremendous uptake of people in the community for the influenza vaccine," Health Minister Roger Cook said.
"If we have the double whammy of bad influenza season and COVID-19 as well, that will have a devastating impact on our community."
Australian Associated Press
