John Bercow has been described as a "playground bully" by MP Shailesh Vara, who is running to replace him as Commons speaker.
The Conservative MP for North West Cambridgeshire, whose constituency covers a large part of Peterborough, said he believes Mr Bercow has "tarnished the role of Speaker with his biasness" and said he insults and demeans his colleagues.
The nine MPs who have put themselves forward to replace Mr Bercow as Speaker took part in a hustings event in Westminster.
Mr Vara was joined by Sir Henry Bellingham, Chris Bryant, Harriet Harman, Meg Hillier, Sir Lindsay Hoyle, Dame Eleanor Laing, Sir Edward Leigh and Rosie Winterton.
Candidates were asked about Mr Bercow and impartiality, and Mr Vara said: "No, Speaker Bercow has not been impartial.
"And frankly speaking, I think he's tarnished the role of the Speaker with his biasness.
"I think what is required is that we need to rewrite the rule book, and make it absolutely clear what the Speaker can and cannot do in difficult circumstances.
"And that is actually to protect the Speaker as much as protecting Parliament.
"Because no matter how well intentioned the Speaker may be, she or he may take a particular decision and those who are aggrieved by that decision are going to feel that it is not fair."
He added: "I would say one other thing that recently we've had a lot of debate about the standards of MPs in the Commons.
"And given that Speaker Bercow has at times behaved like a verbal playground bully in the way that he treats his colleagues - he insults them, demeans them - I think that he loses all authority to lecture to MPs as to how they should behave when his own behaviour is in question.
"So I think that the Speaker should always be courteous and polite, authoritative, yes, but not demeaning to his colleagues."
Sir Henry said he thinks Mr Bercow has been a "fantastic" Speaker, but added: "The problem with John Bercow is that many of the excellent work he's done has been impaired by A, having favourites, I think, in some ways.
"And B, too often grandstanding remarks that frankly are a waste of space and time."
Mr Bryant, who wants to be "an umpire, not a player", said of the Speaker role: "I think having an impartial speaker is absolutely essential to the good functioning of our democracy."
Ms Harman said the role is to be the "champion of Parliament in our parliamentary democracy," adding: "And that's not them being neutral or impartial, it's being absolutely a champion of Parliament."
She said that certainly on any political issue, the Speaker should "set aside their views", adding: "But when it comes to a decision when Parliament is challenged, or when Parliament wants to have its say, or Parliament wants to vote, the Speaker must be the servant of Parliament and not impartial or neutral on that."
Sir Edward said Mr Bercow is "perceived by a large part of the nation not to be impartial" and said the next Speaker needs to be "more in the mould" of former Speaker Betty Boothroyd.
The election of the next Commons speaker will take place on November 4, after Mr Bercow, who has held the office since 2009, takes the chair for the final time on October 31.