NSW reported 34 deaths of patients with COVID-19, while Victoria state saw 14 deaths, and Queensland reported 10 deaths.
Health officials said they believe an Omicron outbreak has peaked in NSW and Victoria, which reported 20,324 and 13,091 new cases respectively on Sunday.
Australian schools return after a summer holiday break in a week.
NSW Premier Dominic Perrottet said parents will be asked to use rapid antigen tests twice a week to check their children for COVID-19, and report any positive result to the school and government.
Millions of the test kits are being distributed to 3,000 schools this week, and students need to be tested before attending the first day of classes, he told reporters in Sydney.
Teachers and high school students will be required to wear masks.
Victoria state has also recommended twice weekly testing of students under its return to school plan.
School staff in NSW and Victoria must be vaccinated for COVID-19, and teachers in Victoria have a deadline of the end of February to receive a booster shot, Victorian health officials said.