The chief constables of West Mercia, Warwickshire and West Midlands Police say they will go before MPs to explain.
The Independent Police Complaints Commission (IPCC) said a misconduct case should have been answered.
Officers are accused of giving a false account of a meeting with Mr Mitchell.
That meeting followed a row with police officers when Mr Mitchell was stopped from riding his bicycle through the gates of Downing Street in September last year.
A transcript of the later meeting showed that, while he admitted swearing, Mr Mitchell denied using the word “pleb” or insulting the police.
But afterwards three senior police officers said he had refused to elaborate on what had happened and should resign.
On Tuesday, the IPCC questioned the “honesty and integrity” of the officers, and said that West Mercia Police had been wrong to conclude they had no case to answer for misconduct.
Home Secretary Theresa May said the IPCC's report “made troubling reading”.
Responding in a joint statement, the chief constables said the watchdog had turned down their offer to play a greater role in the investigation.
They pointed out Mr Mitchell had “never made a complaint to police” and the forces themselves referred the incident to the IPCC.
“We asked for the matter to be independently investigated by the IPCC because we recognise the significant public interest in the matter, however this was declined,” the statement added.
“The IPCC have supervised this investigation throughout and have been invited to reconsider their position on more than one occasion.”
The chief constables said their decisions following the investigation had been “carefully considered” and were backed up with legal advice.
Home Affairs Select Committee chairman Keith Vaz said David Shaw, chief constable of West Mercia Police, would be summoned before MPs next week to explain why misconduct hearings had not been held.
Mr Shaw, along with the chief constables of Warwickshire and West Midlands Police, said they welcomed the opportunity to appear before the committee.
West Mercia police and crime commissioner Bill Longmore said he was seeking a meeting with Mrs May to discuss the IPCC's “critical” statement.
Eight people, including four police officers, have been arrested and bailed over the September 2012 row at the security gates to Downing Street. The Crown Prosecution Service is currently considering charges.
The altercation happened on 19 September when Mr Mitchell was told by police not to take his bike through the main gates. The former Tory chief whip has apologised for an outburst, but has always disputed claims he described policemen as “plebs”.
As the row between the then-cabinet minister and the police intensified, Mr Mitchell met Inspector Ken MacKaill, of West Mercia Police, Detective Sergeant Stuart Hinton, of Warwickshire Police, and Sergeant Chris Jones, of West Midlands Police – acting on behalf of the Police Federation which represents rank-and-file officers – at his constituency office in Sutton Coldfield.
In comments made after the meeting, Inspector MacKaill claimed the former chief whip would not provide an account of the incident and called for his resignation.
The transcript also shows that during that meeting, representatives from the three forces acknowledged that the integrity of their Metropolitan Police colleagues was no longer intact. One of the representatives stated the London officers had “put words in your mouth that are untrue”.
West Mercia Police conducted an internal investigation into claims the three officers had been trying to discredit Mr Mitchell and concluded that there was no case to answer for misconduct or gross misconduct.
It said that there was no deliberate intention to lie to journalists.
On Tuesday, the IPCC – which oversaw the West Mercia investigation – said it disagreed and called for a misconduct panel to be held to determine whether the three officers gave a false account in a deliberate attempt to discredit Mr Mitchell in pursuit of a wider agenda.
However, IPCC deputy chairwoman Deborah Glass added that, because Mr Mitchell had chosen not to make a formal complaint, she was powerless to direct misconduct proceedings.
The Police Federation criticised Ms Glass for her “personal outburst”.