The London mayor, who has previously stated that anyone who swears at police should be apprehended, said an officer's decision to warn Mitchell was correct.
As the row rumbles towards a second week, it emerged on Tuesday that Mitchell also attempted to cycle through the Downing Street gates – in the other direction – the day after the fraught encounter.
A Cabinet Office source told ITV News Mitchell had asked to be allowed through the gates, to enter Downing Street, on Thursday – less than 24 hours after the initial row. Mitchell complied without complaint when permission was refused again.
Speaking at the UN in New York late on Tuesday night, David Cameron said Mitchell was guilty of "deeply regrettable" behaviour towards the police but would remain as chief whip because he had apologised and the officers had declined to lodge a formal complaint. The prime minister indicated that Mitchell would lose his job if there was a repeat of the incident.
Cameron, who summoned Mitchell to a meeting in No 10 last Thursday to explain his behaviour, has accepted the chief whip's explanation that he did not call the police "plebs". Cameron stands by this, despite reading the official police log which has a detailed account of how Mitchell swore at the police and used the word "pleb" last Wednesday.
Asked whether he thought the police were lying, Cameron said: "What I am saying, very clearly, is what happened was wrong and shouldn't have happened. It was deeply regrettable.
"That is why the chief whip has made a very public and clear apology. It is right that he did that. On the basis of that apology, on the basis of the fact also that the police aren't proposing to take matters further, that is how things stand."
Labour is likely to point out that the prime minister is now suggesting he believes a government colleague over armed officers who protect him.
Johnson intervened in the row by rallying to the defence of officers who threatened to arrest Mitchell on Wednesday.
Mitchell has said that he did not use the words attributed to him in media reports of the incident. He admits in private to swearing in front of the officers but denies having described them as plebs.
Speaking at the opening of a library in Ruislip, west London, Johnson said: "If I read the papers correctly, there was a proposal to arrest Mr Mitchell for what he said. That seems to be wholly commonsensical. The Public Order Act does allow for police officers' discretion in this matter. They have obviously decided not to go ahead with it. But it shows the gravity of this offence."
The mayor added: "In my book you shouldn't abuse police officers and I've made that clear loads of times. The crucial thing for me is that Mr Mitchell has now apologised not just once but twice. He's also apologised to the police officer concerned and that underscores how wrong it is for any [of] us to abuse police officers."
Downing Street is annoyed that the media is continuing to focus attention on the episode. Ministers are being discouraged from talking about the incident on air or in the press. A supportive intervention by Kenneth Clarke was seen to have just stoked media interest.
The Sun first revealed in its Friday edition that Mitchell had sworn at officers when they declined to allow him to cycle through the gates on Wednesday.
The police log of the incident was leaked to a newspaper on Monday and it recorded that Mitchell wanted to cycle through the gates, which are usually opened for cars and vans. A female police officer told Mitchell, who insisted that he always cycled through the gates, that it was not policy to open the gates for cyclists.
"After several refusals Mr Mitchell got off his bike and walked to the pedestrian gate with me after I again offered to open that for him," a male colleague of the officer wrote.
"There were several members of public present as is the norm opposite the pedestrian gate and as we neared it, Mr Mitchell said: 'Best you learn your fucking place … you don't run this fucking government … You're fucking plebs'."
The officer who wrote the log said he told Mitchell he would have to arrest him if he continued to swear.
Reports have claimed that before the incident, Mitchell had been at the Cinnamon Club, an upmarket Indian restaurant in Westminster, and after the altercation in Downing Street he went on to the Carlton Club, the Conservative-dominated private-members club.
A letter released by the cabinet secretary, Sir Jeremy Heywood, said that he and the Metropolitan police commissioner Bernard Hogan-Howe have ruled out an inquiry into the incident.
Yvette Cooper, the shadow home secretary, said: "It now looks like there's a cover up going on. Andrew Mitchell's got to tell us what he said, the prime minister's got to tell us what he knew as well ."
Home Office minister James Brokenshire said it was possible that Mitchell and the officer genuinely had different recollections of what happened.
"I have got no reason to doubt the recollections of either Andrew Mitchell or the police officer concerned," he told Sky News. "It may well be that they can both honestly believe that their recollection of those events is as has been recorded."
• This article was amended on 26 September 2012. The original referred to Ruislip as in south London. This has been corrected
guardian.co.uk © Guardian News and Media Limited 2010
image: © BackBoris2012