Warwickshire Chief Constable Andy Parker has said he was "embarrassed" that his officers had become involved in a heated anti-cuts campaign in the wake of the Plebgate incident.
"My officers got involved in a political campaign which was ill thought-through and has led to a lot of public confidence issues for us," he said.
"I would certainly like to apologise to Mr Mitchell because this added to the already big impact of the Plebgate campaign and it is embarrassing that my force was involved in the way it was."
The chief constable of West Mercia Police has apologised for the findings of an investigation that initially found three Police Federation officers who met Andrew Mitchell had no case to answer for misconduct.
Chief Constable David Shaw has overturned the earlier finding and written a personal letter of apology to the former Chief Whip.
He has asked for another chief constable to be called in to review the decision not to take action against the three officers.
He told the Home Affairs select committee: "Clearly the buck stops with me and I have to be accountable for a huge range of things that go on.
"It's unedifying and it hurts the force."
Chief Constable David Shaw of West Mercia Police has written to former Chief Whip Andrew Mitchell to offer "a profound unreserved apology" over the 'Plebgate' meeting.
He told MPs from the home affairs select committee, he wrote a letter on Monday which was "a personal apology from me".
"It was a profound unreserved apology for the impact what has happened has had on him", he added.
The Chief Constable of the West Mercia Police has offered "a profound unreserved apology" to Andrew Mitchell for what happened.
– Detective Sergeant Stuart Hinton from Warwickshire Police
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.
We certainly didn't lie intentionally.
Three police officers who have been accused of giving a misleading account of a meeting with former chief whip Andrew Mitchell have defended their actions to MPs.
Police Federation representatives Inspector Ken MacKaill, Detective Sergeant Stuart Hinton and Sergeant Chris Jones apologised only for their haste in speaking to the media straight after the meeting in October last year.
They told journalists Mr Mitchell refused to tell them exactly what he said during a foul-mouthed confrontation with officers in Downing Street the previous month.
But they were later accused of misleading the public over the account of the 45-minute meeting, which was recorded by the politician.
Conservative MP James Clappison has asked three Police Federation officers why they did not ask Andrew Mitchell for more information about the encounter at Downing Street if they were not satisfied with his account.
Detective Sergeant Stuart Hinton from Warwickshire Police said: "I wasn't there to conduct a police interview with Mr Mitchell. We were having a meeting to try and clear the air and to try and sort out what had happened".
He added that when they told the media the former Chief Whip has not explained himself properly, what they said was "a reasonable reflection of what we understood had been said in the meeting".
The Police Federation representative, Inspector Ken MacKaill from West Mercia Police, has told MPs, "I do not accept that it was a case of gross misconduct" over its account of a meeting between Andrew Mitchell at which he was present.
He said: "I gave what I believed was an accurate account of the meeting to the media but I subscribe to the apology that I should not have done it in the way I did".
The Police Federation's Sergeant Chris Jones has denied misleading the public over the meeting that took place with former Chief Whip Andrew Mitchell, telling MPs "We did represent that meeting correctly when we emerged from it".
Chair of the home affairs select commitee Keith Vaz said to Sergeant Jones, "you have nothing to apologise for?", to which he replied "correct".