Democratic presidential candidate Elizabeth Warren has challenged her fellow candidate Michael Bloomberg to release all former employees from agreements that keep them from speaking out in public.

Speaking after an acerbic debate in which she castigated Mr Bloomberg for his alleged treatment of female employees over the years, Ms Warren told an audience at a CNN town hall that she was giving Bloomberg a chance to let his former employees talk publicly.

“This is an election for president of the United States, and transparency here is important. So, I used to teach contract law. And I thought I would make this easy.

“I wrote up a release and covenant not to sue, and all that mayor Bloomberg has to do is download it – I’ll text it – sign it, and then the women or men will be free to speak and tell their own stories.

Ms Warren then read out the contract’s “relevant language”:

"Bloomberg and the company release any and all obligations contained in any agreement, including but not limited to any employment, settlement, severance or nondisclosure agreement, between Bloomberg and/or the company and any other person, to the extent those obligations preclude the other person from disclosing information relating to sexual harassment, discrimination, or other misconduct at the company or by Bloomberg himself.

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"Under this release, it is now the other person’s choice to disclose such information or not.

“I think that the mayor should sign this, and that we all have a right to see.”

Mr Bloomberg has acknowledged that several former employees – many of them women – have signed nondisclosure agreements upon leaving his employment.

During the televised presidential debate, which featured Mr Bloomberg’s widely panned first appearance, Ms Warren repeatedly brought up the issue of nondisclosure agreements as she pummelled him over his record as an employer.

Mr Bloomberg responded: “None of them accuse me of doing anything, other than maybe they didn’t like a joke I told. And let me just – and let me – there’s agreements between two parties that wanted to keep it quiet and that’s up to them. They signed those agreements, and we’ll live with it.”

The billionaire candidate is struggling to recover from the fallout from his debate performance, in which he struggled to respond to fierce attacks from all the other candidates.