Senior MPs are calling for the Government to look at introducing emergency legislation so police and crime commissioners such as under-fire Shaun Wright can be sacked.
Appearing before the Commons Home Affairs Select Committee, Mr Wright said he intended to stay in his job, claiming that resigning would have been the easy option.
South Yorkshire's police and crime commissioner has resisted demands to quit in the wake of a damning inquiry into child abuse in Rotherham spanning 16 years, including five where he was in charge of the town's children's services.
Those calling for him to step down include Prime Minister David Cameron, Home Secretary Theresa May and Labour leader Ed Miliband as well as his deputy, Tracey Cheetham, who stepped down herself in protest at his failure to go.
Keith Vaz MP, chairman of Commons Home Affairs Select Committee
Now, committee chairman Keith Vaz is writing to Ms May "because it is unsatisfactory in our view that someone should be able to say to the public who elected them 'I'm just carrying on'".
Mr Vaz called for Mr Wright's "immediate resignation", and the chairman of the Association of Police and Crime Commissioners, Nick Alston, told Sky News "his position was untenable".
The Jay Report outlined how at least 1,400 children had been subjected to trafficking, rape and other sexual exploitation between 1997 and 2013.
It also said their plight had been ignored by range of agencies, including police, councillors and council officials.
Twenty-five more victims have come forward since the report was published last month.
Former South Yorkshire chief constable Meredydd John Hughes
Mr Wright told MPs the problem of child sexual exploitation was not flagged up to him as a significant issue during his time as a councillor with responsibility for Rotherham's children services from 2005 to 2010.
But Mr Vaz responded by saying: "We don't accept you didn't know."
Mr Wright told the MPs: "I basically think that resigning would have been, perhaps, the easy option given the last fortnight with the various criticisms that have been made and the effect that that's had on both myself and my family."
He said it was his responsibility to the people of South Yorkshire to continue in his post and said no one had raised any questions about his conduct since his 2012 election - a suggestion rejected by Mr Vaz.
David Crompton admits things should have been done differently
Earlier, a former South Yorkshire police boss admitted he had "no idea" about the scale of child abuse in Rotherham while he was in charge.
Meredydd John Hughes, who was chief constable between 2004 and 2011, told MPs he was "embarrassed" at the failure to act to stop it.
Appearing before the same committee, he faced some tough questioning from MPs who said child exploitation "on an industrial scale" had taken place on his watch.
There were heated exchanges with Mr Hughes, who told the committee: "I can say with honesty that at the time I was both deputy and chief constable, I had no idea of the scale and scope of this type of organised crime."
He said he had not seen three of four reports being examined by their inquiry until recently.
He said: "Some of those reports ... I frankly felt sick last night when I read them. I am not immune to the ideas that this is a hideous crime and I am deeply embarrassed."
But he was rebuked by Mr Vaz, who told him his denials were "impossible to believe" in the face of "evidence of the most compelling nature" to the contrary.
After a 32-year career with the police, Mr Hughes said he had "singularly failed the victims of these victims".
His successor, Chief Constable David Crompton, was also questioned and told MPs: "I accept things should have been done differently in the past."
But he also told the committee: "Things are better now than they used to be."
Mr Vaz had taken the unusual step of requiring the witnesses to swear an oath before the hearing started.