Morrison wants to get "planes flying around Australia".
Prime Minister Scott Morrison has ramped up calls for state leaders to set a border opening timetable with coronavirus infections at low levels.
The federal government is applying fresh pressure on states to restart interstate travel amid calls for more help to be directed to aviation.
"We need to get planes flying around Australia," Mr Morrison told parliament.
"If you want to see planes flying around Australia, we need to open up these domestic borders."
He wants premiers to nominate a July date, in line with national cabinet's target for the third stage of eased restrictions.
There were seven new cases reported across Australia on Wednesday, four in Victoria and three in NSW.
The average national daily increase has been at 0.06 over the past three days.
Just 20 people remain in hospital with the disease, three of whom are in intensive care.
The current COVID-19 figures.
Victorian teenager home after two nights missing in bushland.
A Victorian teenager is home with his family after spending two nights missing in dense Victorian bushland in freezing temperatures.
William Callaghan, 14, who is non-verbal with autism, is alive and well after he was found on Wednesday.
The youngster raced ahead of his family at Mt Disappointment on Monday and became separated from them, sparking a huge search.