Beleaguered Tory Chief Whip Andrew Mitchell on Monday denied calling police officers "fucking plebs" during an altercation in Downing Street last week.
The millionaire Tory MP insisted that he did not make the comment, despite police logbooks reportedly showing he called officers "plebs" and swore at them repeatedly.
Downing Street resisted calls on Monday for an inquiry into the incident after the Cabinet minister apologised publicly to police officers for subjecting them to a tirade of verbal abuse.
A Number 10 spokesman said the Prime Minister believed that Mr Mitchell had done the right thing in apologising and thinks a line should now be drawn under the affair.
Asked if the PM still had full confidence in Mr Mitchell as chief whip, the spokesman said: "Yes."
However, Metropolitan Police Federation chairman John Tully said Mr Mitchell was effectively accusing the officers of lying and called on Mr Cameron to launch an investigation.
"Clearly Mr Mitchell is denying using certain words, effectively now impugning the integrity of the police officers," he told Sky News.
"I think that is very serious. I think the Prime Minister or Downing Street officials should hold an inquiry and if Mr Mitchell is proved to have lied, then he should be sacked."
Labour too called for an inquiry, while Deputy Prime Minister Nick Clegg said it was right that Mr Mitchell should explain "fully and in detail" what happened during the altercation after officers refused to allow him to cycle through the main gates of Downing Street.