However, friends of the former chief whip have been alarmed by the fact that No 10 did not release the revelatory CCTV footage – which casts doubt on the validity of the police officers' account – when Mr Mitchell was fighting for his career.
One said the Prime Minister had left the former chief whip "swinging in the wind".
Speaking during a trip to Afghanistan, Mr Cameron said Tories had "a lot of sympathy" for Mr Mitchell given the latest twist in the saga, which has now been rebranded "plodgate".
In October, the MP for Sutton Coldfield resigned his Cabinet role after continued coverage of an incident a month earlier when police officers refused to allow him to cycle through the main Downing Street gates.
While Mr Mitchell admitted swearing at the officers, he denied their claims that he had called them plebs and morons. Two corroborative emails later confirmed the police officers' account almost word for word.
However, it has transpired the emails came from a serving police officer, who was not even at the scene at the time.
One claim made in the emails, that the incident had been witnessed by a crowd of people outside the Downing Street gates, was refuted by subsequently released CCTV footage, which showed no such crowd.
Two people, including one serving police officer, have since been arrested. Scotland Yard insists it is determined to get to the truth and 30 officers are now working on the case.
Mr Cameron revealed Mr Mitchell had visited him at No 10 on Monday night, the day before the revelations surrounding the CCTV coverage were revealed.
"He was calm and rational," explained the PM, "but feels obviously disturbed by what seems to have happened and is keen to get to the bottom of it. His mood was pretty calm and reasonable given what are pretty extraordinary revelations."
He added: "It has been an extraordinary development, frankly, to find a police officer apparently posing as a member of the public, pretending to have been outside Downing Street at the time and then trying to blacken the name of a Cabinet minister."