Prime Minister Scott Morrison says imagery of social media posts, allegedly made by Liberal Lyons candidate Jessica Whelan, appear "to have been doctored" and would be referred to the Australian Federal Police.
Ms Whelan has denied the posts - which contain sexist and racist material - were made by her, and yesterday called for an investigation into the matter.
Mr Morrison was in Tasmania to attend Agfest and make a number of announcements about changes to the Pharmaceutical Benefits Scheme and a raft of proposed agriculture, forestry and fisheries initiatives.
In an afternoon press conference at Norwood, he was asked if Ms Whelan should be stood down as their candidate.
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"The imagery that we have found, that has been presented to us, appears to have been doctored," Mr Morrison said, adding that the matter is being referred to the AFP.
"This is a matter that will be the subject to an investigation," he said.
Mr Morrison also defended Ms Whelan for not answering questions during her visit to Agfest as they were "not doing a press conference" earlier in the day.
In question time on Thursday, Premier Will Hodgman was asked repeatedly about the posts which he labelled as "without a doubt abhorrent", though said he had not heard of them prior.
"There is no doubt that those words, if used by any person, that they should not be endorsed as a candidate in this upcoming federal election," he said.
Labor leader Rebecca White said Ms Whelan should not continue as the endorsed Liberal candidate for Lyons, adding that several of the comments were left on her professional Facebook page two years ago and were clearly made by Ms Whelan.
"Any claims that will be made by your party that this post was "digitally altered" cannot be based in any fact," Ms White said.
Franklin Greens MHA Dr Rosalie Woodruff said Mr Hodgman needed to address the matter because, as Liberal leader, he was one of the people responsible for approving all candidates standing in the federal election.
"Facebook posts bearing Ms Whelan's name have said hateful and Islamophobic comments including the statement that women who supported Islam should be mutilated and sold as slaves," Dr Woodruff said.
Speaking in Burnie, deputy Australian Labor Party leader Tanya Plibersek said the comments were "extraordinarily racist" and it was vital for the Prime Minister to show leadership by disendorsing Ms Whelan.
"Racism is racism is racism," Ms Plibersek said.
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