The move came as Mr Mitchell's colleagues sought to put an end to the controversy while Downing Street insisted Prime Minister David Cameron still had full confidence in his Chief Whip.
Eric Pickles, the Conservative Communities Secretary, said Mr Mitchell should not be sacked simply for being a "guy on a bicycle who lost his rag".
The Tory minister also received support from Nick Clegg. The Deputy Prime Minister made clear that while what the Conservatives' chief enforcer of party discipline did was very wrong, he should be allowed to draw a line under the incident.
It seems clear the strategy being adopted by Tory HQ is for the Chief Whip to keep a low profile in the hope other matters will blow the row off the front pages.
However, Yvette Cooper, the shadow home secretary, has asked Sir Jeremy Heywood, the Cabinet Secretary, to investigate Mr Mitchell's outburst, claiming his account was unravelling by the day.
Mr Mitchell allegedly told police officers at Downing Street's gates: "Look, I'm the Chief Whip, I work at Number 9 (Downing Street)," before explaining they are there to help ministers.
A friend of the minister said: "He does not dispute he lost it a bit. It was in frustration at the episode and not aimed directly at the officers.
"It was the fourth time he had been at Downing Street that day – he is frequently allowed to use the main gate on his bike. He is absolutely not accusing anyone of lying." While Mr Mitchell admits swearing, he flatly denies addressing the police officers, who refused to let him through the Downing Street gates on his bicycle, as "plebs".
The friend added: "He realises there may be differing versions of what was said but he is adamant he did not use the words he is reported to have used."
However, Ms Cooper said: "We now know Andrew Mitchell swore at police officers who were doing their job protecting Downing Street.
"This is completely unacceptable behaviour from a Cabinet minister and a half-hearted private apology is clearly insufficient," she declared.
"Given the justified anger and concern from police officers of all ranks, Mr Mitchell should apologise publicly immediately," she said.
"Andrew Mitchell's account of what went on is unravelling day by day and we need to know exactly what happened.
"Everyone is already deeply concerned that a senior cabinet minister is reported as dismissing police officers doing an important security job as 'plebs'.
"It is really important the Prime Minister does not compound this by dismissing the testimony of police officers and the evidence from their notebooks without proper investigation."
She added: "From the reports we have seen, it appears that either the Chief Whip used very offensive language to dismiss an officer on duty and has not told the public the full story. Or alternatively, Mr Mitchell and the Prime Minister are saying the testimony of police officers who protect Downing Street cannot be trusted or should be ignored. Either of those alternatives is extremely serious."
Mr Mitchell, a keen cyclist, was reported to also have called the police "morons" and reportedly told them in colourful language that they needed to learn their place.
The top Tory has denied using the words attributed to him but accepted he treated the police on duty at the time with disrespect. He added: "I have seen the supervising sergeant and apologised and will also apologise to the police officer involved."