About a dozen MPs from both May's Conservative Party and the main opposition Labour Party have been accused of harassment in recent days and the government has admitted serious failures in reporting procedures.
At closed-door talks in the House of Commons on Monday, May will be meeting party leaders including her main rival, Labour leader Jeremy Corbyn.
Speaking to the Confederation of British Industry ahead of the meeting, May said she wanted "a new, common, robust and independence grievance procedure for parliament".
Defence secretary Michael Fallon resigned last week and First Secretary of State Damian Green, May's deputy, is under investigation by the government over the claims, some of which date back several years.
"We need to establish a new culture of respect at the centre of our public life," May said.
She said the new culture should be "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".
But she also said "people's careers cannot be damaged by unfounded rumours circulated anonymously online" after many claims made via social media.
"Of course, people can be friends with their colleagues and consensual relationships can develop at work - this isn't about prying into private lives," she said.
'Watershed moment'
On Friday, May announced a new code of conduct for the Conservative Party under which several MPs were referred for investigation this weekend.
Two Labour lawmakers have also been suspended, another is facing an investigation by the party and a fourth has apologised for making women feel "uncomfortable".
One change that has been mooted is to make MPs' staff direct employees of parliament rather than of the politicians themselves - an anomaly that has made some harassment victims reluctant to come forward.
Home Secretary Amber Rudd said on Sunday the scandals were a "watershed moment" that was "clearing out" inappropriate behaviour but the interior minister denied May's minority government was at risk.
Fallon announced his resignation on Wednesday after apologising for touching a journalist's knee in 2002.
Another journalist alleged this weekend that Fallon had "lunged" at her after a lunch in 2003.
She said she reported the incident to Downing Street this week, and he resigned hours later.
Green meanwhile is being investigated for his own alleged inappropriate behaviour towards a journalist, which he strongly denies.
Rudd confirmed that the probe had been widened to include a newspaper report on Sunday that "extreme" pornographic material had been found on his parliamentary computer in 2008.
Green has strongly denied the story in The Sunday Times and accused the police source behind it of trying to cause him political damage.
Also on Sunday, Conservative lawmaker Chris Pincher resigned from his role as a whip - enforcing party discipline - and referred himself to the party's complaints procedure and the police following allegations over his behaviour.
The move followed a report in The Mail on Sunday newspaper that Pincher was accused of making an unwanted pass at former Olympic rower and Conservative activist Alex Story.
