Former chief whip Andrew Mitchell said he will be "pleased" to meet three chief constables whose forces are at the centre of a row that erupted in the wake of the Plebgate scandal.
Three more junior officers involved in the dispute have remained defiant despite the leaders of their forces issuing public apologies and the renewed threat of disciplinary action.
Police Federation representatives Inspector Ken MacKaill, Detective Sergeant Stuart Hinton and Sergeant Chris Jones appeared before MPs yesterday and would apologise only for their haste in speaking to the media straight after the meeting in October last year.
But Mr Mitchell welcomed the apologies from the the chief constables of the three forces that they represent - Warwickshire, West Mercia and the West Midlands.
Mr Mitchell who resigned from the Cabinet as the row over an altercation with police at the gates of Downing Street engulfed him last year, said: "I'm very grateful to the three chief constables - David Shaw from West Mercia, Andy Parker from Warwickshire and Chris Sims from the West Midlands - for the apology that they have given to me and my family.
"I will be pleased to meet them as they have requested."
Following a meeting in October last year the three Police Federation representatives told journalists that Mr Mitchell refused to tell them exactly what he said during a foul-mouthed confrontation with officers in Downing Street the previous month.
The three were later accused of giving a misleading account of the 45-minute meeting, which was recorded by the politician.
Det Sgt Hinton told the Home Affairs Select Committee: "We showed poor judgment in speaking to the media immediately following the meeting with Mr Mitchell.
"I think we are all happy to take the criticism on the chin for that. What we should have done is given ourselves an opportunity to debrief the meeting."
He added: "We certainly didn't lie intentionally."
Sgt Jones said he did not believe they had done anything wrong, while Mr MacKaill stood by the initial account of what happened in the meeting.
The decision not to press ahead with misconduct charges against the officers following the meeting was challenged by the Independent Police Complaints Commission (IPCC), which said there were issues of ''honesty and integrity'' among the three representatives of the Police Federation.
The three men held the private meeting with Sutton Coldfield MP Mr Mitchell about claims that he had called officers guarding the Downing Street gates "plebs".
Chief Inspector Jerry Reakes-Williams, who conducted the internal investigation, told MPs he still believes the officers have a case to answer over accounts they gave of the meeting.
He said: "I did find a case to answer for misconduct and that's still my view."
Mr Mitchell met the three officers in his constituency office on October 12 last year after he was accused of calling officers guarding Downing Street ''plebs'' in a rant as he was asked to cycle through a side gate on September 19.
The Tory MP said he wanted to meet Mr MacKaill, Det Sgt Hinton and Sgt Jones to ''clear the air''.
A secret recording made by Mr Mitchell shows that he apologised for swearing at the police officers but denied using the word ''plebs'', while in comments made after the meeting Mr MacKaill claimed the former minister refused to provide an account of the incident.
Mr Reakes-Williams, who deals with professional standards for Warwickshire and West Mercia police, told MPs: "My view is that, taken as a whole, the comments made by the federation representatives did have the impact of misleading the public as to what happened in that meeting."
But he said for a charge of gross misconduct - which carries the possible sanction of dismissal - he would have to have been sure that the officers had gone to the Sutton Coldfield meeting with the "premeditated" intention of lying about Mr Mitchell, he said.
The IPCC's deputy chairwoman Deborah Glass told the Home Affairs Committee that she was "absolutely astonished" when a final report came back from the three forces recommending that the officers had no case to answer.
The three officers rejected any suggestion that they plotted together to bring down Mr Mitchell.
"I absolutely refute that suggestion," said Mr MacKaill.
As the three officers concluded their evidence, Mr Vaz warned them that giving inaccurate evidence to the committee would amount to a contempt of Parliament, and added: "We have found your evidence most unsatisfactory."
After the marathon session Mr Vaz indicated a further three senior officers from the forces could be called to give evidence about a meeting which agreed there was no case to answer following the federation representatives' meeting with Mr Mitchell.