Speaker John Bercow is facing calls to quit after a report into bullying in the House of Commons.
Women and Equalities Committee chairwoman Maria Miller and senior Labour MP Sir Kevin Barron both said new leadership was needed.
It comes after Dame Laura Cox said bullying and harassment were not being dealt with in the Commons due to a culture of "acquiescence and silence".
MPs will debate her report later, after Mr Bercow granted an urgent question.
Mr Bercow's office declined to comment on Mrs Miller's call for him to quit.
On Monday his spokeswoman said the Commons Commission, which he chairs, would meet urgently to consider a response to the "serious" report.
And the House of Commons executive board has apologised for "past failings" and said it was "committed to changing our culture".
The report, by former high court judge Dame Laura Cox QC, said radical changes were needed in the way cases of bullying and harassment were dealt with in the House of Commons.
It did not refer to claims of bullying against Mr Bercow, which he denies.
Sir Kevin, who stepped down on Monday after eight years in charge of the Commons Standards Committee, told the BBC: "It's quite clear there has been a lack of leadership over a considerable part of time in term of the culture that makes... the Houses of Parliament, for some people, not a safe place to work, and I think the Speaker has responsibility for that."
Speaking on BBC Radio 4's Today programme, Mrs Miller said there was "no option but root and branch change of management".
As well as chairing debates between MPs, the Speaker is the highest authority of the House of Commons and must remain politically impartial.
Labour MP Barry Sheerman defended Mr Bercow against what he said was a "shabby attack".
Shabby attack on John Bercow @thetimes sad to see Kevin Barron siding with far right Brexiteers & their vile campaign against our Speaker.— Barry Sheerman (@BarrySheerman) October 16, 2018
And Labour's shadow foreign secretary Emily Thornberry told Sky News that because of Brexit, this was "absolutely not the time to be changing Speaker", adding: "We do need to have all hands at the deck at the moment."
"People I know and respect say he's a fine Speaker," she said.
"He has been responsible for introducing a lot of reforms so long in coming, they are very much to his credit."
But the leader of the FDA union, which represents senior civil servants, accused Ms Thornberry of putting "party politics before people".
Completely disingenuous from @EmilyThornberry. Just last month, you were speaking at the TUC 150th Anniversary dinner about workers' rights. Now you're happy to ignore Dame Laura Cox's urgent calls and put party politics before people. Which side are you on? https://t.co/Udkj85nwBu— Dave Penman (@FDAGenSec) October 16, 2018
Dame Laura was appointed in March after a Newsnight investigation uncovered complaints about a number of MPs, including Mr Bercow - allegations which he denies.
On Monday Dame Laura told the BBC Mr Bercow and other people in positions of leadership, such as the clerk of the House of Commons and the director general of the House of Commons, should read the report "very carefully".
Senior figures, she said, needed to ask themselves "do I understand that radical change is needed, can I deliver that and will the staff have confidence that I can deliver that change?
"If they can't answer 'yes' honestly to those questions they should each of them be considering their position."
In her report, she described the House of Commons as a "stark reminder of how bad things used to be" and said there was a culture of "deference, subservience, acquiescence and silence".
A spokeswoman for Mr Bercow said it was "a serious report into a serious subject which deserves a serious response".
She added: "The House of Commons Commission will meet as a matter of urgency in the coming days to consider the report and our response to it."
A separate "review of of historical allegations" is also under way, and in July MPs backed a new grievance procedure and behaviour code.
The House of Commons executive board said the report made "difficult reading" and added that there was no place for bullying and harassment.
It said it was "determined to learn lessons" from the report, adding that it will meet on 22 October to consider the findings.