Mr Crompton said he ‘remains committed’ to leading the force through improvements to its child protection practices.
It comes after former Sheffield Council leader Lord Scriven said it was time for Mr Crompton to step down following a critical new report by Her Majesty’s Inspectorate of Constabulary.
Lord Scriven said the report showed the police are still failing vulnerable children and he will be raising the issue in the House of Lords.
But Mr Crompton said this evening he would not be going.
He said: “HMIC has made it clear that senior leaders are demonstrating the determination to make the required improvements.
“I remain committed to leading the force through those improvements and, with 19 people charged with more than a hundred CSE related offences in the last three months, I’m confident that we are making an impact on dealing with the root cause of the problem.”
Mr Crompton tonight also received the backing of South Yorkshire police and crime commissioner Dr Alan Billings.
Dr Billings said: “This is not the time to destabilise the organisation by threatening dismissals. But I do expect the senior officers to work closely with me in putting right what still needs to be done and to do it with a great sense of urgency.”
He added: “The Jay report on child sexual exploitation in Rotherham fell like a thunderbolt last August. It led every police force and local authority in the country to re-examine its work in this area, past and present.
“I came into this office as a direct result of that report and since then have worked hard with the police and other agencies to make progress.
“Some good things have been done. We increased the number of people working in child sexual exploitation. We are enabling police staff to sit alongside and work directly with social workers from each of the four local authorities. Arrests have been made and people charged. They will come to trial later in the year.
“I set up a panel of victims, survivors and their families who are just starting to work directly with the police to help them improve some of the things the recent inspector’s report commented on. They will help victims to be treated with dignity and respect.”
Lord Scriven today repeated his calls for Mr Crompton to resign in light of the most recent report criticising the performance of South Yorkshire Police.
He said: “This is the fourth time now we have had such a report.
“The time for reports and reviews has gone - the time for action is now and South Yorkshire Police management are not delivering it.
“The man at the top has got to go.”
South Yorkshire Police was heavily criticised in last year’s Jay Report, which exposed how at least 1,400 children had been subjected to child sexual exploitation in Rotherham between 1997 and 2013.
Professor Alexis Jay criticised officers for ‘regarding many child victims with contempt’.
This week it was revealed HMIC inspectors had audited 28 recent child protection cases - with just two assessed as good, 19 requiring improvement and seven inadequate.
The Independent Police Complaints Commission is currently investigating how South Yorkshire Police officers dealt with cases in Rotherham, with more than 100 complaints made against over 40 past and current officers. The National Crime Agency has also begun a major fresh investigation of allegations of child sexual exploitation in the town, which is expected to potentially last up to three years.