Lichfield MP Michael Fabricant took to social media website Twitter to ask a series of questions about the altercation between Mr Mitchell and police officers at the gates of Downing Street, following the release of CCTV footage of the encounter.
And he warned that there should not be a "witch-hunt" against the police, after questions were raised over the account given by officers.
Metropolitan Police Commissioner Bernard Hogan-Howe has promised a "ruthless" investigation "no matter where the truth takes us", after breaking off from his holiday to be briefed on progress.
Mr Mitchell claimed he was the victim of a deliberate attempt to "toxify" the Conservative Party and destroy his career
He was forced to quit his Cabinet post in October amid a storm of protest over claims he abused officers when they asked him to use a pedestrian side-exit rather than open the Downing Street gates. He has confirmed that he swore during the exchange, but has firmly denied claims he addressed officers as "plebs" and "morons".
Last week Scotland Yard opened an investigation into a possible conspiracy against the MP after it emerged that an email to deputy chief whip John Randall, purporting to come from a civilian witness backing up the allegations, was in fact written by another officer. And supporters of Mr Mitchell said that CCTV images taken from Downing Street and the Foreign Office showed that there was not enough time for the supposed exchange to have taken place as reported.
The Sutton Coldfield MP detailed his recollection of the conversation in an article for the Sunday Times yesterday.
But Mr Fabricant said that the CCTV footage - as broadcast last week by Channel 4 News and Dispatches - lasted 46 seconds, while the words recalled by Mr Mitchell would take only around 20 seconds to speak.
And he suggested that people were ready to believe that Mr Mitchell may have been abrasive because of pre-existing views of his personality.
"The problem Andrew Mitchell has is that if Michael Gove had been accused, it would be hard to believe. He is invariably polite and courteous," wrote Mr Fabricant in a series of messages on Twitter spanning several hours on Christmas Eve.
"If Andrew Mitchell was stitched up by the police, it is unforgivable. But will we ever know exactly what was said and by whom?.
"Witch-hunts are unfair. The witch-hunt against Mitchell was wrong if story was embellished. But the witch-hunt now against the police not good.
"CCTV reveals AMitchell meets police at 19:36:08. There is discussion. AM leaves gates at 19:36:54. Ch4 claims `20 secs'. Bad sums, boys.
"I suspect the truth is 6 of one and half a dozen of the other. NO-ONE comes out of it smelling of roses: neither the police nor Andrew.
"What I am saying is CCTV reveals about 46 secs of conversation. Read Andrew's account in Sunday Times. 20 secs? What else was said???"
Mr Fabricant said that the differing accounts of the affair raised a number of questions:
"CCTV shows 46 second interaction between AM and Police. AM's report only takes 20 seconds. What else was said?," he asked.
"The CCTV outside FCO has had its time code removed. Why?
"Why does CCTV footage show someone walking away and then walking back again to Gates?
"Downing Street CCTV footage does show at least one person outside listening to exchange. Will he/she come forward to help investigation?
"We know that the email to Randall was probably false, but does that make police at Gates liars? That does NOT follow logically."
As other Twitter users responded to the Tory MP, he wrote: "What is my motive? To get to the truth and overcome poor journalism by some. Neither Andrew nor police should be vilified until facts known."