Prime Minister Scott Morrison has now sought to distance his team from Jessica Whelan, who has been vying for the seat of Lyons.

"Her views were her views, and they do not represent the views of the party I lead," he told reporters in Melbourne on Friday.

Ms Whelan maintains she did not make one of the Islamophobic comments that emerged under her name this week and has referred the "doctored" Facebook post to federal police.

But the Tasmanian branch of the Liberal Party says Ms Whelan has accepted she made "some of the other posts in question" and offered her resignation on Friday, which it has accepted.

"Clearly these posts are inappropriate, and the Liberal Party was not aware of their existence until they were reported," a party spokesman said.

The Hobart Mercury uncovered two new Facebook posts bearing the candidate's name and photograph on Thursday, one of which calls for a national vote on banning Muslim immigration.

The other argued Tasmania should not accept refugees from Syria and Iraq.

The candidate was already under fire over another post that argued women who supported Islam should be mutilated and sold as slaves.

"Round them up Donald, cut their clitoris' off & sell them to Muslims in Muslim countries & cancel their passports. You'll make a mint," it stated.

A party spokesman initially said Ms Whelan denied making the post and that it appeared to have been digitally manipulated.

In a statement of her own on Friday, Ms Whelan said she will continue legal action over posts wrongly attributed to her.

She lamented death threats directed at her and her family.

"It saddens me that people who put their hand up to represent the people of Australia are subjected to such vicious personal attacks from their opposition born directly from their fear of losing."

Ms Whelan will run as an independent, WIN News understands.

Acknowledging Ms Whelan's defence on Thursday, Mr Morrison said it was not hard to believe that an image could be doctored.

But on Friday, he said the Liberals had acted quickly once new information that had not been disclosed by the candidate emerged.

"What that says is, we're prepared to deal with these issues."

He urged Labor to do the same with the embattled candidate for Melbourne Luke Creasey, who shared a rape joke and made offensive remarks about women online.

Lyons has been in contention for the Liberals, who needed to overcome a 3.8 per cent margin to win the seat.

The party is now urging voters to elect Nationals candidate for the seat, Deanna Hutchinson.

Australian Associated Press