The Prime Minister said "the conduct of… officers was not acceptable".
The row centres on claims that Mr Mitchell called police officers on duty in Downing Street "plebs".
Mr Mitchell, who lost his job during the fallout from the claims, has always denied saying the word.
The latest development involves a meeting between Mr Mitchell and three officers from the Police Federation, which represents officers.
Following the discussion one of the officers called for Mr Mitchell to resign, saying he had refused to elaborate on the altercation.
Unknown to him, however, Mr Mitchell had recorded their conversation and could prove he had strongly denied saying the word "pleb".