Australian MP Andrew Laming says he is stepping aside from duties to undertake cultural sensitivity training after allegations of harassing women online.

Two women accused him of slandering them, with one saying it had left her feeling suicidal.

PM Scott Morrison had ordered Mr Laming, a backbencher in his Liberal Party, to apologise in parliament for his "disgraceful" behaviour.

Mr Laming has not stepped down as an MP.

Any decision that sees him go will have consequences for the government, as it could cost Mr Morrison's coalition its parliamentary majority.

In his statement, Mr Laming said: "I will step down from all parliamentary roles effective immediately and complete both the counselling courses I committed to; as well as additional clinical counselling, and ask for privacy while that is completed." He said he would have "more to say on my future" after his awareness training.

The episode is the latest challenge to Mr Morrison's government, in a month when a series of rape, misconduct and sexism allegations have rocked Australian politics.

The prime minister has faced mounting pressure over his response to the allegations and broader cultural problems within politics.

Last week, tens of thousands of people marched in protests against the mistreatment of women in Canberra and wider society.

A Channel Nine TV report aired on Thursday heard from two women who said they'd been repeatedly harassed by Mr Laming - who is their local Brisbane MP - on Facebook.

Alix Russo said he had targeted her with verbal abuse, and falsely accused her of fraud.

The report included screenshots of Mr Laming's comments, many of which attacked Ms Russo and ridiculed her business situation.

"Unfortunately for you, I make the rules and you follow them," the MP wrote in response to one of her comments.

Another woman, Sheena Hewlett, said she and her husband - a local councillor - were also harassed by the MP.

Mr Laming apologised on Thursday for his social media posts.

"I want to unreservedly apologise to both Ms Hewlett and Ms Russo and I express my regret and deep apologies for the hurt and distress that that communication may have caused," he said.

Mr Morrison said: "I called him into my office yesterday, and told him to apologise and deal with it - and he has."

The opposition Labor Party called Mr Laming's comments "shocking" and said he should resign.

Mr Laming on Saturday also faced an accusation from a Brisbane woman that he had taken a mobile phone photo of her while she was bending over at a landscape supply business in 2019.

The woman contacted Mr Laming via Facebook to complain, the Sydney Morning Herald reported. It said the MP had replied that he was not trying "to be rude" in taking the image.

Many Australians - particularly women - have long accused politicians and the political environment of being toxic towards women. They have called for sweeping cultural changes.

Focus on the issue was ignited in February, after a former political adviser said she had been raped in 2019 by a male colleague in a minister's office.

Brittany Higgins, 26, reported the allegation to her boss - Defence Minister Linda Reynolds - but said she had felt pressure not to report it to police.

Her story inspired other women to come forward, including four others with allegations against the same man.

Later, Attorney General Christian Porter identified himself as the subject of a separate 1988 rape allegation - which he strongly denies. Police closed an investigation because his accuser is no longer alive.

Both Mr Porter and Ms Reynolds are on sick leave, but retain Mr Morrison's support.

Earlier this week, a government adviser was fired after a video showed him performing a sex act on a female lawmaker's desk.

Network Ten reported that parliament's prayer room had also been used by politicians and staff for sex.

Mr Morrison has condemned the reports and vowed to "get this house in order", but he has faced persistent accusations of not listening to women's concerns.

Ms Higgins has accused him of using "gaslighting" language and doubting victims.

Earlier this week, she also demanded an investigation into claims that the prime minister's office had sought to undermine her reputation.

Mr Morrison told Channel Nine on Thursday: "I may not have always got it as much as people would like me to, but I assure you, I am doing everything I can to understand it as best I can."