Scott Morrison says Liberal MPs are satisfied with how the party is dealing with claims of bullying and intimidation, particularly towards women.
But Labor leader Bill Shorten has another idea.
"The best place for the Liberal Party to resolve all of these toxic, poisonous issues - the best place to get it out of their system - is a good, long stint in opposition," he told parliament on Monday.
Liberal senator Lucy Gichuhi is threatening to name those responsible under parliamentary privilege this week, while her Victorian colleague Julia Banks has decided to quit politics at the next election.
Liberal Party elder Warren Entsch is urging his colleagues to name the MPs who bullied them.
"I'm glad to see Lucy's prepared to stand up and name them and I hope Julia does the same," the Queensland MP said.
"The small number that's out there ... they need to be fingered and they need to be held accountable for their actions."
But Mr Morrison said he had spoken to Mr Entsch about how the party whips were dealing with the behaviour.
"I know he's fully satisfied with the way that the party is managing all issues that are germane to the internal running of the Liberal Party," the prime minister told parliament.
Mr Shorten said the bullies must not remain anonymous.
"Bullies are not entitled to the protection of secrecy, they do not deserve a deliberate silence from the prime minister of Australia," Mr Shorten told parliament.
Liberal ministers are also divided over whether their party should introduce gender quotas to ensure more women are elected to parliament.
Less than a quarter of federal Liberal MPs are women, compared to almost half of Labor politicians.
Businessman Andrew Bragg, who quit his job to run for Liberal preselection to replace Malcolm Turnbull in Wentworth, has dropped out of the race and called for a woman to take the seat.
"I believe the Liberal Party should preselect a woman and my withdrawal can pave the way," he posted on Facebook.
"I believe these recent events and comments have changed the mood and accordingly I will withdraw my nomination."
Mr Bragg said comments from Ms Banks had "genuinely shocked" him, and she was an enormous loss to public life.
There's speculation Mr Bragg stood aside in return for a prominent spot on the party's NSW Senate ticket.
Australian Associated Press
