The Australian bishops' conference said it would not put blanket bans on Mass, including for Holy Week, calling the issue a "diocesan matter."
In a short statement on its website, the Australian government said new measures announced by Prime Minister Scott Morrison for nonessential gatherings included religious services, even Mass.
Dioceses have increasingly placed bans and restrictions on Masses since March 16, with a surge in announcements March 18 and 19.
Bishops in the state of Victoria said that suspending Masses was difficult, "and every encouragement is offered as clergy and parish staff seek to explain sensitively to our people the reasons why Mass will not be offered as a public celebration," a note on the Archdiocese of Melbourne website said.
The Archdiocese of Brisbane suspended Masses and released Catholics from their Sunday obligation. It said it would livestream Masses from the cathedral.
In some places, weekday Masses -- attended by fewer people -- are still being celebrated, with restrictions on how to receive the Eucharist.
However, Catholic schools in New South Wales, Australia's largest state, will remain open temporarily after the government warned it would cut funds if they closed. Some parents chose not to send their children to school.
Countries that appear to have been most effective in slowing and containing COVID-19 shut schools as part of their programs to combat the disease.
Gavin Abraham, spokesman for the Australian Catholic Bishops' Conference, told Catholic News Service the conference was monitoring information about COVID-19. The first of two sessions of the church's Plenary Council is due to be held in Adelaide in October. This falls just outside the latest guidelines from Australian Prime Minister Scott Morrison of a "six-month" process to try to get through the COVID-19 crisis.
"We will continue to monitor the situation and make decisions about the first assembly when advice relevant to October 2020 is clearer," Abraham said.