Forcing children to wear masks is causing massive physical and psychological harm that can only be defined as child abuse," Mr Kelly wrote on Facebook.
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In another post, he said denying ivermectin to patients was responsible for "over 100,000 deaths" in Mexico. He has also called for the use of hydroxychloroquine, a drug also backed by US President Donald Trump.
Health Minister Greg Hunt would not refer to Mr Kelly by name on Tuesday when asked about his claims, advising people instead to listen to official advice.
Professor Kelly said he had worked in the past on the use of ivermectin to treat river blindness in Africa and knew it was effective for that purpose, as well as against scabies, but it had no proven use against COVID-19.
"There is no evidence at the moment that it has any benefit or any use in relation to the prevention or treatment of COVID-19," he told a press conference on Wednesday.
