Damien Green made his comments after it was claimed they misrepresented their meeting with Mr Mitchell in his Sutton Coldfield constituency.
The Home Office minister spoke out about the comments given by the representatives from the West Midlands, West Mercia and Warwickshire divisions.
They attended a private meeting with Mr Mitchell after he was accused of calling their Downing Street colleagues plebs.
Mr Green said their version of the meeting was "palpably untrue".
Speaking on the BBC's Andrew Marr show, Mr Green said: "He deserves an apology. Let's start with the people who left his office and said things that if you read the transcript were palpably untrue."
Asked if he was referring to the three police officers who met with Mr Mitchell when the allegations first emerged, he replied: "Absolutely, those three should apologise."
Prime Minister David Cameron has also said the police owed Mr Mitchell an apology over the affair, saying their behaviour was not acceptable.
Mr Green was asked if Mr Cameron also owed Mr Mitchell an apology, as it was suggested he only stood down from his role because he was effectively pushed out by the Prime Minister.
However, Mr Green disagreed. He said: "He didn't, because Andrew Mitchell resigned. He resigned."
He added: "Let's do this in order: let's find out what the facts are, what the CPS (Crown Prosecution Service) say, whether there was a criminal conspiracy, whether there's more police disciplinary action to be taken against those at the gate at Downing Street; all those questions need to be answered first."
Home Secretary Theresa May has also warned the scandal risked jeopardising public trust in the police in England.