She said she had given the Labor leader a deadline of Thursday to respond to a request to revoke the border ban before proceeding to the High Court.
The High Court challenge,which has yet to be filed,would be led by Queensland law firm Mahoneys and NSW barrister Guy Reynolds,SC,who are expected to appear on behalf of a group of Queensland residents affected by the ban. The case would not be funded by taxpayers.
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In a letter on Tuesday to Queensland's Chief Health Officer,Dr Jeannette Young,and copied to the Premier,Mahoneys says it acts for"various persons who consider that the border ban is invalid under the Commonwealth Constitution".
"We request that you undertake to revoke the border ban by 4pm on[Thursday] 28 May 2020 and otherwise undertake not to enforce it,"the letter says.
"If you do not give that undertaking,and you do not otherwise satisfy us that the border ban is valid,we expect to receive instructions to commence proceedings in the High Court of Australia seeking a declaration that the border ban is invalid."