David Cameron has told Tony Blair that it is in the "national interest" for him to quit now as prime minister.
Tony Blair has yet to set a date for his departure
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.
Those health policies had reduced waiting lists by 400,000, and education policies "have seen the best school results ever".
He also said it was in the national interest to "continue to reduce crime, not as his [Conservative] government did, put it up".
Mr Cameron described the Cabinet as being divided over foreign policy as they fight to be the next deputy prime minister, while others were "joining picket lines" in protest at hospital cuts.
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.
"Isn't that the whole problem with this government? In any organisation if you have got long-term problems, you can't have a short-term chief executive.
"In these circumstances, a minister like the home secretary cannot plan for the future," Mr Cameron said.
Mr Blair responded: "I can certainly guarantee that he will continue to make the investment in prison places, for example, in community support officers.
"Just last week we had the latest crime statistics, which show yet again a fall in recorded crime.
"We now have a situation where, over the last 10 years, whatever the challenges in the Home Office, crime has actually fallen. It doubled under the Conservative government you supported."