More than 12,000 young people in New South Wales tested positive in the second week of term, but the state will relax testing requirements for school students.
From Monday week, Dominic Perrottet said the testing will be on-demand.
The tests will be given to parents in two drops.
The packs are there for families and staff to use at their discretion, for example, when a student is feeling unwell with a sore throat or cough, or if family members are sick.
The free tests will be given to teachers.
Sarah Mitchell, the education minister, said there had been no school closings since students returned.
She said that testing children twice a week was not an easy task and that she would like to thank all of the parents and caregivers.
Additional RAT kits will be given to early childhood staff.
There were 21 Covid-related deaths and 5,582 new cases in the state on Sunday.
Of the 1,280 patients treated in the state's hospitals, 77 are in intensive care and 35 are in need of ventilation.
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The health authorities say there have been deaths of men and women. Fourteen were aged in their 80s, five in their 70s, three in their 60s and one in their 50s and 90s.
Three were not immunised.
In the final term of the year, 3 to 4% of people exposed to a positive case in school and early childhood settings contracted Covid, compared to 70% in residential settings, according to research conducted by the National Centre for Immunisation Research.
Victoria extended the requirement for twice-weekly rapid testing until the end of the term.
On Sunday, Victoria recorded 4,867 new Covid infections and nine virus-related deaths.
Travelers who have been vaccinated will be able to enter Australia from Monday for the first time in two years.
The prime minister told reporters at the airport that they were going from cautious to confident when it came to travel.
He said there are 1.2 million people around the world who arevisaed up and can come to Australia.
In the next 24 hours some 56 flights are going to touch down in Australia, and that number is only going to grow.
My message to tourists is to pack your bags and come and have a great time. Don't forget to bring your money with you because you will find a lot of places to spend it.
The reopening of borders is welcomed by business.
Steve Hughes, HSBC head of commercial banking, said that the reopening will allow companies with international interests to conduct business more easily.
Mid-sized firms which have reached the limits of their domestic growth will have renewed confidence to consider offshore expansion.
International travellers that are not vaccine-free will be able to use the new $200m Quarantine hub in Victoria on Monday.
The purpose-built Victorian Quarantine Hub will be vital to how we manage Pandemics today and into the future, according to the police.
There is a 500-bed Quarantine centre built in the state of QUEENSLAND which is likely to house unvaccinated international arrivals.