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The PM will say in a speech later that people should know their complaints will be investigated properly.
It comes as several Conservative and Labour MPs are investigated over claims of sexual misconduct.
On Sunday Conservative MP Chris Pincher stepped down as a government whip after allegations about his behaviour.
Mr Pincher has also referred himself to police and the Conservative party's complaints procedure following newspaper reports of allegations about his conduct in 2001 made by a party activist.
It follows the resignation of Michael Fallon as defence secretary following complaints about his behaviour and amid a Cabinet Office inquiry into the conduct of First Secretary of State Damian Green.
Dover MP Charlie Elphicke has been suspended from the party after "serious allegations" against him were referred to the police - he denies any wrongdoing - and several other Conservative MPs have been referred to the party's disciplinary committee after media allegations about their conduct.
Labour have also suspended an MP - Kelvin Hopkins who denies claims he made inappropriate physical contact with a Labour activist in 2004 - and is investigating a formal complaint made against Clive Lewis.
The party has also launched an independent investigation after Labour activist Bex Bailey said she had been raped at a party event in 2011 and discouraged by a senior official from reporting the attack.
Mrs May will use a speech at the Confederation of British Industry (CBI) conference on Monday to say: "We need to establish a new culture of respect at the centre of our public life.
"One in which everyone can feel confident that they are working in a safe and secure environment, where complaints can be brought forward without prejudice and victims know that those complaints will be investigated properly.
"Political parties have not always got this right in the past. But I am determined to get it right for the future."
She is due to meet other party leaders later to discuss setting up an independent grievance procedure for Parliament.
"Those working for Members of Parliament should not have to navigate different party systems depending on their employer's political affiliation," the prime minister will say in her CBI speech.
"What has been revealed over the last few weeks has been deeply troubling - and has understandably led to significant public unease.
"Women and men should be able to work free from the threat or fear of harassment, bullying or intimidation.
"But for too long the powerful have been able to abuse their power, and their victims have not felt able to speak out."
Labour leader Jeremy Corbyn has also condemned Westminster's "warped and degrading" culture of sexual harassment during a speech on on Sunday at his party's North West conference in Blackpool.
"We must say, no more. We must no longer allow women, or anyone else for that matter, to be abused in the workplace or anywhere else," he added.
Meanwhile, Mr Green, Mrs May's most senior minister, is to be interviewed as part of the Cabinet Office investigation into his conduct.
The inquiry was triggered after Kate Maltby, who is three decades younger than him, claimed he "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.
Mr Green said any allegation that he made sexual advances to Ms Maltby was "untrue (and) deeply hurtful".
The inquiry was broadened after the Sunday Times reported that a statement prepared by ex-Metropolitan Police Assistant Commissioner Bob Quick alleged pornography was discovered by officers searching Mr Green's parliamentary office following a spate of leaks of Home Office information in 2008.
Mr Green said the claims were "completely untrue" and "political smears".