Theresa May said any allegations about serious sexual abuse in Parliament should go to the police, as she promised a new “independent” process to handle complaints.
The PM said she was “deeply concerned” by recent reports about alleged harassment and abuse at Westminster.
She invited Labour’s Jeremy Corbyn and other party leaders to a meeting to agree a new grievance procedure.
Mr Corbyn said trade unions should be involved to support staff.
Two ministers, meanwhile, have denied claims on a list, thought to have been drawn up by Westminster staff and researchers, detailing a range of mostly unproven allegations about 40 Conservative MPs.
Following a range of recent allegations, including claims of a lack of support for those making complaints, Mrs May has written to party leaders calling for the “serious, swift, cross-party response this issue demands”.
The PM said a “common, transparent independent grievance procedure” for all those who work in Parliament was needed and that it “cannot be right” for policies to vary between parties.
A dedicated support team should be available to all staff, she said, and it should recommend all criminal allegations be reported to the police.
Speaking at Prime Minister’s Questions, Mr Corbyn said he was happy to meet the PM to discuss it, with a meeting scheduled for Monday evening.
The SNP’s Ian Blackford said his party would also work with the government “to ensure that we have a system we can be proud of”.
During PMQs, Labour’s Lisa Nandy said that three years ago she had raised concerns with Mrs May that party whips’ offices – whose job is to keep the party’s MPs in line and voting a certain way – had used sexual abuse allegations to demand loyalty from MPs.
She later tweeted the exchange in question, which related to events in the 1970s and was raised at the time the inquiry into historical child abuse was being launched.
Responding at the time in 2014 Mrs May, who was home secretary, said political parties would be included in the inquiry and that “every area where it is possible that people have been guilty of abuse” would be looked at.
Responding to Ms Nandy in PMQs, she said she would look back at the questions raised, adding: “I will say to her that I am very clear, that the whips’ office – I hope this goes for all whips’ offices across this House – should make clear to people that where there are any sexual abuse allegations that could be of a criminal nature that people should go to the police.
“It is not appropriate for those to be dealt with by whips’ offices; those should go to the police – that continues to be the case.”
Ahead of PMQs, Mrs May’s deputy, Damian Green, said allegations of inappropriate behaviour towards a female activist were “completely false” and he said he had instructed libel lawyers.
Tory activist Kate Maltby had written in the Times that he “fleetingly” touched her knee in a pub in 2015, and in 2016 sent her a “suggestive” text message.
Former Conservative minister Anna Soubry said Mr Green should stand down while the allegations are investigated, but Small Business Minister Margot James told BBC 5 live: “I’ve read the article in the Times today, and I certainly don’t think that it warrants anyone’s resignation, temporary or otherwise, in my opinion.”
Two other ministers, Dominic Raab and Rory Stewart, hit out at the list of unproven allegations about Tory MPs.
Justice minister Mr Raab said he had sought legal advice over the “false allegations”, which he described as a “form of harassment”.
In an article on his website, he added: “I appreciate the Westminster list will encourage a further media feeding frenzy against MPs. I also recognise that there are undoubtedly some very disturbing allegations out there, which need to be taken seriously.
“At the same time, for anonymous individuals to compile and publish, or allow to be published, a list of vague, unsubstantiated and – in my case – false allegations is wrong.
“It is also a form of harassment and intimidation, although of course I am not suggesting it is the same or equivalent. Still, accountability should mean properly investigating any reports of abuse, without irresponsibly smearing those who have done nothing wrong.”
Mr Stewart said claims about his behaviour towards a female member of staff were “completely untrue”.
The researcher publicly backed this up, saying the aid minister was “never anything other than completely professional and an excellent employer”.
Labour, meanwhile, has launched an independent investigation into an activist’s claim that she was discouraged by a party official from reporting an alleged rape at a party event in 2011.