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.”
Deloitte administrators overseeing bids for Virgin Australia are concerned potential buyers may not proceed without guarantees of continued support.
But Mr Morrison is adamant certainty around domestic travel increasing will be more important.
“If we’re concerned about Virgin employees, it is very important that we open up the domestic borders in this country,” he said.
He wants premiers to nominate a July date, in line with national cabinet’s target for the third stage of eased restrictions.
Labor’s transport spokeswoman Catherine King dismissed concerns about borders, saying the JobKeeper wage subsidy scheme needed to be extended beyond the September cut-off.
“We’re now almost in the 11th hour and we’re yet to see any response from the government at all to the Virgin administrators, let alone to the 16,000 workers and their families who rely on Virgin,” she told reporters.
A move to extend JobKeeper to university workers failed in the Senate on Wednesday evening.
Greens senator Mehreen Faruqi said parliament should reverse the malicious move to exclude up to 30,000 workers.
“With the stroke of a pen the government could reverse their absurd exclusion of university from this program and begin the hard work of protecting the sector,” she told the upper house.
The motion was defeated 31 votes to 30.
Mr Morrison has left the door open to removing other sectors from JobKeeper when it announces the finding of a review on July 23.
“Where there is a better way to do things, we won’t step aside from doing them in a better way,” he said.
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.
While 102 people have died in Australia from coronavirus, more than 6740 of the 7276 diagnosed have recovered.