The Independent Police Complaints Commission (IPCC) said Inspector Ken MacKaill, Detective Sergeant Stuart Hinton and Sergeant Chris Jones should have faced misconduct hearings for lying about what Mitchell said in a private meeting about the row last year.
At prime minister's questions Cameron said the conduct of the officers, who were representing the Police Federation, was "not acceptable".
He said Mitchell was "owed an apology, the conduct of these officers was not acceptable" and "these things should be properly investigated".
The prime minister backed the stance taken by Home Secretary Theresa May, who has insisted West Mercia Police force was "quite wrong" not to take disciplinary action.
The force's chief constable, David Shaw, has been summoned to give evidence to the Home Affairs Select Committee on the issue next week.
The committee's chairman Keith Vaz raised the row with Cameron in the Commons, saying the IPCC report was "damning".
Cameron said: "I agree 100% with what the Home Secretary said yesterday and I think we should be clear about what we are discussing here.
"The whole case about what happened outside 10 Downing Street, that's with the CPS and we have to leave that on one side until they make their decision.
"What's being discussed here is the fact that ... the former chief whip had a meeting with Police Federation officers in his committee where he gave a full account of what had happened, they left that meeting and claimed he had given them no account at all.
"Fortunately this meeting was recorded so he has been able to prove that what he said was true and what the police officers said was untrue."
Cameron added: "He is owed an apology, the conduct of these officers was not acceptable, these things should be properly investigated, as the Home Secretary has said."
It was right for Vaz's committee to "discuss this with the chief constables concerned and try to get to the bottom of why better redress has not been given".