A Conservative MP has made a formal complaint to the Commons standards watchdog Kathryn Stone about the behaviour of Speaker John Bercow.
Last week MPs blocked Ms Stone from probing allegations that Mr Bercow bullied staff, which he denies.
But James Duddridge, a long-time critic of Mr Bercow, is calling on her to investigate comments reportedly made about Commons leader Andrea Leadsom.
Mr Bercow has admitted "muttering" the word stupid during a Commons row.
Mr Bercow, who has been Speaker since 2009, has faced calls to apologise over unconfirmed reports he used the words "stupid woman" in connection with Mrs Leadsom following a row over the scheduling of a rail debate.
In a statement on Monday, he said he used the word stupid, as a "muttered aside", in the context of "summing up how I felt about the way that the day's business had been conducted".
He praised Mrs Leadsom's "political ability and personal character" but insisted he would continue to do his job and, where necessary, take issue with ministers' handling of parliamentary business.
'Set an example'
In his letter to the Commissioner, Mr Duddridge said he believed Mr Bercow's actions breached the Commons' 2009 code of conduct, which obliges MPs to act in a way which upholds public trust and confidence in Parliament and does not bring the institution into disrepute.
"We cannot let the current situation of intimidation and bullying from such a senior figure whom we should look to set an example and act as arbitrator," the former foreign office minister and MP for Rochford and Southend East wrote.
"The perpetrator cannot be allowed to have so much power over the House, its members and staff who work in the Commons. It is essential that the Speaker steps aside from chairing and participating on all matters related to bullying."
He also asked for a call to evidence over "intimidating behaviour which I and other members have witnessed repeatedly over the years".
The Commissioner's office confirmed it had received a complaint.
It said she would "consider whether the matter is within her remit and, if it is, whether there is sufficient evidence to justify beginning an inquiry".
Last week a committee of MPs voted against an investigation into allegations of bullying by Mr Bercow against former staff.
The standards committee voted by three to two that Ms Stone should not hold the investigation following a separate complaint. Mr Bercow's office has rejected all the claims.