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The Conservative leader made the call during Prime Minister's Questions in the House of Commons, saying: "When is he going to realise it is all over?"
He said ministers were "treading water" and the PM's authority "draining away".
Mr Blair, who will quit by September, said it was in the national interest to continue with a strong economy and Labour's health and education policies.
The Tory leader also highlighted the current situation at the Home Office, where Home Secretary John Reid is battling with overcrowded prisons among other problems.
Mr Reid has said he needs two and a half years to turn the department around, said Mr Cameron, but he asked whether Mr Blair could guarantee the home secretary would be in the job beyond the next four months.