Tony Blair has criticised the home secretary over a lack of action on the "respect agenda", according to a leaked report in the Sunday papers.
Tackling school discipline forms part of the 'respect agenda'
It says the prime minister told Charles Clarke at a meeting that more must be done to address low-level disorder.
Downing Street insisted it was "absurd" to suggest Mr Blair was unhappy with Mr Clarke's handling of the issue.
Conservative David Davis blamed "seven years of failed policy", while the Lib Dems said it was "passing the buck".
The leaked document, obtained by the Sunday Telegraph and Sunday Times and dated 21 June, contains minutes of the previous day's meeting on the subject in Downing Street.
BBC correspondent Guto Harri said the language used suggested that not enough progress was being made on tackling low level disorder, truancy and school discipline.
"On respect the prime minister said this was a real issue for the public," the minutes are reported as saying.
"We needed to address it now otherwise a sense of fatalism would set in."
Newspaper reports say Mr Blair also expressed frustration that the recent debate about ID cards had been dominated by considerations of cost and that sentencing policy was shaped by the number of prison places available.
Number 10 and the Home Office both deny the meeting involved in any way a "dressing down" for Mr Clarke.
"The prime minister has complete confidence in the home secretary and to suggest otherwise is absurd," the Downing Street spokesman said.
Defence Secretary John Reid told Sky News: "Charles hasn't gone soft".
"The prime minister very often works very closely with a secretary of state, as he did with me on health," he said.
But shadow home secretary David Davis said: "It is not good enough for the prime minister to rebuke his latest home secretary for the public perception of his actions.
"These are the results of eight years of failed policy, not seven months of inadequate spin."
Liberal Democrat home affairs spokesman Mark Oaten said it showed the government's approach to anti-social behaviour is not working.
"As ID cards become more and more unpopular, Tony Blair's comments are the start of a ministerial pass the buck," he continued.
"No-one in government will want to end up taking the blame for this expensive fiasco."