Theresa May will meet other party leaders next week to agree plans on tackling sexual abuse and harassment in Westminster.
The Prime Minister said MPs from all parties are “deeply concerned” about allegations that have emerged in recent days and she has invited political counterparts to talks on setting up a grievance procedure.
Labour leader Jeremy Corbyn said he was happy to take part in the process.
Mrs May told the Commons: “I’ve written to all party leaders inviting them to a meeting early next week so we can discuss a common, transparent, independent grievance procedure for all those working in Parliament.
“We have a duty to ensure that everyone coming here to contribute to public life is treated with respect.”
Mrs May has ordered an inquiry into claims made against her deputy, Damian Green, after he became the most senior politician yet to be caught up in a tide of allegations and rumours.
The Cabinet Office investigation was launched after activist Kate Maltby, who is three decades younger than the First Secretary of State, told The Times that Mr Green “fleetingly” touched her knee during a meeting in a Waterloo pub in 2015, and a year later sent her a “suggestive” text message after she was pictured wearing a corset in the newspaper.
Damian Green is to be investigated (David Cheskin/PA)
Mr Green, who was sat near Mrs May during Prime Minister’s Questions, said any allegation that he made sexual advances to Ms Maltby was “untrue (and) deeply hurtful”.
Tory former minister Anna Soubry said Mr Green should stand down while the allegations are investigated and claimed that in “normal circumstances” he would be suspended.
But business minister Margot James said she did not think the allegation “warrants anyone’s resignation, temporary or otherwise”.
A Downing Street spokesman said Mrs May had asked Cabinet Secretary Sir Jeremy Heywood to “establish the facts and report back as soon as possible”.
Anna Soubry said Mr Green should stand down while the allegations are investigated (Yui Mok/PA)
Meanwhile, Labour has launched an independent inquiry into claims that prominent activist Bex Bailey was discouraged by a party official from reporting an alleged rape at a Labour event in 2011 on the grounds it might damage her political career.
Mr Corbyn vowed he would allow “no tolerance” of sexism, harassment or abuse after Ms Bailey spoke out about the party’s failure to support her.
Aged 19 at the time of the alleged attack, she said she felt too scared and ashamed to report it to the police, but eventually summoned up the courage to tell a senior party official.
Labour said it takes the allegations “extremely seriously” and has launched an independent inquiry by general secretary Iain McNicol into the claims that she was not given adequate support by the party.
Labour’s Lisa Nandy said she asked Mrs May three times to act over claims party whips were using reports of abuse to control MPs instead of dealing with the issues.
She said: “Three years ago I brought evidence to her in this House that whips had used information about sexual abuse to demand loyalty from MPs.
“I warned her at the time that unless real action was taken, we risked repeating those injustices again today. On three occasions I asked her to act, and on three occasions she did not.”
Mrs May said whips’ offices 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”.