Some of the 30,000 airline passengers stranded by cancellations caused by a cloud of ash from a Chilean volcano are now on the move, with Virgin Australia resuming flights.
But Qantas has cancelled all flights in and out of Tasmania and New Zealand for the rest of Monday.
All flights in and out of Melbourne have been cancelled until 1pm, the company announced on its Twitter feed.
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"Obviously, with regard to Melbourne, we'll look to make a decision later this morning on the outlook for the rest of the day, beyond midday," the spokesman told AAP.
"We regret the inconvenience but we've got very strict risk assessment and safety procedures.
"At this stage we just don't consider it safe to operate."
The spokesman said more than 10,000 passengers had been affected by the flight cancellations on Sunday and Monday morning, a number that is now expected to increase.
He said passengers should check the Qantas website for further information on their flights.
Airservices Australia spokesman Matt Wardell said the ash cloud continued to cover Tasmania and parts of Victoria, including Melbourne, on Monday.
"It's at quite a high level, about 7.5km to 11km high, and it's diffusing and slowly moving northeast," Mr Wardell told AAP.
"Air traffic management officers will continue to monitor the cloud during the day and provide advice to airlines."
VIRGIN AUSTRALIA RELIEF
Virgin Australia said it will operate flights out of Melbourne, Tasmania and New Zealand from 7am (AEST) on Monday.
"Overnight we have been monitoring closely the situation and we now believe that conditions are safe to operate," group executive operations Sean Donohue said in a statement.
A spokeswoman said the airline would be consolidating its flights in an attempt to get as many passengers away as possible.
Mr Donohue added that passengers with reservations for travel on Monday should check the Virgin website before leaving for the airport.
The plume of ash that has been blown from Chile's erupting Puyehue volcano towards New Zealand and southern Australia has caused chaos with the major airlines cancelling flights and disrupting the travel plans of thousands of passengers.
It's feared that it could take days to get flights back to normal and the passengers to their destinations.
Qantas has cancelled all flights between Melbourne, Tasmania and New Zealand until 10am (AEST) but it will reassess the situation early on Monday.
The airline has advised customers who were booked on cancelled flights not to head to the airport on Monday and it will contact them to rebook them on the next available services.
Jetstar has cancelled 64 international and domestic flights on Monday. The cancellations affect flights to and from New Zealand, Tasmania and Melbourne.
A spokesman said all flights to and from those destinations up until 10am were cancelled. The airline is currently reviewing the situation about how to proceed after 10am, a spokesman said.
Tiger Airways has suspended all domestic flights until 11.30am (AEST) on Monday, a statement on the airline's website said.
The airline said it would continue to monitor the situation and would provide an update on Monday's scheduled flights at 9am (AEST).
"Tiger Airways will continue to review the situation and will resume flights as soon as it is possible, however safety comes first," the statement said.
Airservices Australia spokesman Matt Wardell said the ash cloud continued to cover Tasmania and parts of Victoria, including Melbourne, on Monday.
"It's at quite a high level, about 7.5km to 11km high, and it's diffusing and slowly moving northeast," Mr Wardell told AAP.
"Air traffic management officers will continue to monitor the cloud during the day and provide advice to airlines."
