Theresa May has vowed to overhaul disciplinary procedures in Parliament after mounting reports of abusive and inappropriate behaviour towards women.
It follows claims International Trade Minister Mark Garnier asked his secretary to buy sex toys and called her "sugar tits".
A list of 13 MPs facing harassment has been circulating at Westminster, according to the Daily Telegraph.
The Guido Fawkes website claimed Tory aides had compiled a spreadsheet of 36 Conservative MPs - including 20 ministers - accused of inappropriate behaviour.
Mrs May has ordered a Cabinet Office inquiry into the claims against Mr Garnier, which were reported by the Mail on Sunday.
The paper quoted the 53-year-old as saying he did not deny the claims.
She is also facing calls to suspend a second senior Conservative, former Cabinet minister Stephen Crabb, over reports he sent explicit messages to a 19-year-old woman he interviewed for a job.
David Cameron reportedly tried to get MPs to voluntarily sign up to a code of conduct which could have given parliamentary staff extra protection from sexual harassment, but was met with resistance.
Health Secretary Jeremy Hunt told ITV's Peston On Sunday Mr Garnier will be investigated to see if he broke the ministerial code.
He said he recognised the accusation that politicians do not practice what they preach.
"I think people at home will be quite angry about this. In our own back yard we don't live up to (those) standards.
"My view is if you had a daughter leaving university ... as a mum or a dad you would want to be confident she wouldn't be subjected to this kind of behaviour."
Mrs May has called the allegations "deeply concerning"and warned that anyone found to have behaved inappropriately would face "serious action".
She said the Conservative Party had offered MPs a code of conduct on a voluntary basis, but that it had no legal standing and was "not fit for its intended purpose".
In a letter to Speaker John Bercow, the prime minister said the current grievance system for dealing with complaints by MPs' staff lacked "teeth" as there was no contractual requirement for MPs to follow its procedures.
"I do not believe that this situation can be tolerated any longer.
"It is simply not fair on staff, many of whom are young and in their first job post-education," she wrote.
"It is vital that the staff and the public have confidence in Parliament and resolving this employment irregularity on a cross-party basis can play an important role in this.
"I would be grateful if you would be able to use your office to assist me in doing all we can to ensure that the reputation of Parliament is not damaged further by allegations of impropriety."
Labour leader Jeremy Corbyn has called for MPs who engage in a "warped and degrading culture" to be held accountable for their actions.
In a speech on Saturday he said the culture where the abuse of women is accepted and normalised "thrives in the corridors of power, including Westminster".
Liberal Democrat leader Sir Vince Cable signalled his support for Mrs May's initiative, saying: "Parliament clearly needs improved procedures to respond to allegations of harassment."
The former chairman of the Committee on Standards in Public Life, Sir Alistair Graham, also backed the move but warned against making the system too complicated, and questioned Mrs May's suggestion of a mediation system.
"This could be a turning point," he told BBC Radio 4's Westminster Hour.
"But the danger is you just get an accretion of more and more systems which just makes the whole arrangement unworkable - which is why I'm a great believer in simplicity, clarity, and making sure that when complaints are made they're investigated very quickly."