Two cruise ships were ordered to leave Australian waters on Thursday, after a liner that docked in Sydney Harbour last week became the primary source of infection for the country's coronavirus outbreak.

While remaining well below the levels seen elsewhere in the world, the number of cases in Australia is starting to pick up speed, rising to nearly 2,800 infections and 12 deaths nationally.

Cruise ships have become a flashpoint after 147 of 2,700 passengers who were allowed to disembark from Carnival Corp's Ruby Princess later tested positive for COVID-19, a blunder that has highlighted official tensions in the handling of the crisis.

State authorities have clashed with the federal government over who was responsible for the oversight, adding to tensions and conflicting public advice over matters including virus testing and school closures.

Some state leaders have also flagged they are willing to push for tougher restrictions on social activities if Prime Minister Scott Morrison's government does not move fast enough.

"Because of the lack of consistent messaging, because people had been flouting the earlier advice regarding social distancing measures, we need to move further and quickly to ensure that what we're seeing around the world doesn't mimic and occur on front doors," Australian Medical Association President Tony Bartone told reporters.

In Australia, the Ruby Princess outbreak sparked anger over why passengers, more than a dozen showing flu-like symptoms, were cleared to disembark without basic health checks.

The Western Australia state government said Thursday that nobody would be permitted to disembark the German-operated MV Artania after seven of 800 foreign passengers on board tested positive for COVID-19 unless there was a "life-threatening emergency."

"This ship needs to leave immediately," Premier Mark McGowan said. "Our position is clear, we are not going to have a Sydney Harbour fiasco on our watch."