The Tory MP denies calling members of Scotland Yard's Diplomatic Protection Group "plebs" after they refused to let him cycle out through the main Downing Street gates.
However the newspaper says the police report shows that he did use the derogatory term, and repeatedly swore at the officers.
The new claims came hours after Deputy Prime Minister Nick Clegg said Mr Mitchell should keep his job as the Government's chief enforcer, unless new information emerged about what was said.
He told the BBC's Andrew Marr show: "Unless something comes to light about the rival versions, about what was and what was not said that I don't know about, I think he should apologise in full - he's done that, that's right - and draw a line under it in that way."
Labour has asked Downing Street's most senior civil servant to investigate the issue, claiming Mr Mitchell’s account of the row is "unravelling by the day".
Shadow home secretary Yvette Cooper said cabinet secretary Sir Jeremy Heywood must also release the full accounts of what was said during the outburst.
The row was made public by The Sun on the day Prime Minister David Cameron headed to Manchester to pay his respects to murdered PCs Nicola Hughes and Fiona Bone.
The paper claimed that he had said to the officers: "Best you learn your f****** place. You don't run this f****** Government. You're f****** plebs."
In a statement on Friday Mr Mitchell said: "On Wednesday night I attempted to leave Downing Street via the main gate, something I have been allowed to do many times before.
"I was told that I was not allowed to leave that way. While I do not accept that I used any of the words that have been reported, I accept I did not treat the police with the respect they deserve.
"I have seen the supervising sergeant and apologised, and will also apologise to the police officer involved."