However, a steady flow of tests may not hit local stores until late-February.
The free test scheme allows concession holders access to 10 tests in three months, with a maximum allowance of five per month.
"There is also another 22 million arriving just for pharmacy through those wholesalers in the first three weeks of February," Mr Twomey said.
"(The supply shortage) is going to be fixed...Today is phase 1 or tranche 1. More will come online over the coming days and weeks."
There remains sustained pressure on the federal government to offer the RATs free nationwide.
Meanwhile, 6 million of the at-home kits will be accessible through NSW schools, after a plan to keep kids in classrooms was revealed by Premier Dominic Perrottet.
Students and teachers will undergo rapid testing twice a week.
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