Tony Blair should take personal responsibility for the "shambles" at the Home Office, Conservative leader David Cameron has told MPs.
Tony Blair accused the Tories of opposing tough measures
Home Secretary John Reid has described his department as "unfit for purpose".
Mr Cameron said that was at odds with Mr Blair's insistence the immigration system had been transformed.
At a Commons session so stormy the Speaker threatened to suspend it, Mr Blair said much progress had been made but more was needed.
Labour had repeatedly proposed "tough" measures which had been opposed by the Conservatives.
Amid rowdy scenes Commons Speaker Michael Martin took the unusual step of warning that he could suspend the prime minister's question session if "he heard any more hissing".
Mr Cameron said it would not wash for Mr Blair to claim the Immigration and Nationality Directorate had transformed when Mr Reid said it was "unfit for purpose".
Liberal Democrat leader Sir Menzies Campbell also said Mr Blair seemed to disagree publicly with his home secretary.
The prime minister said Labour had inherited a system from the Conservatives where asylum applications took 22 months to decide and failed asylum seekers were not deported.
REID'S EIGHT PRIORITY AREAS:
Ensure individuals in contact with criminal justice, immigration and asylum systems have a unique personal number
Make it an obligation for suspects and criminals to declare their nationality
Instruct all agencies to refer other categories of foreign national cases to immigration directorate
Order officials to audit-trail all policy criteria governing which individuals should be considered for deportation
All decisions on deportation to be made according to the most robust interpretation of international obligation requirements
Clear procedures demanded for dealing with foreign national prisoners held in Scotland and Northern Ireland
Officials to make arrangements for considering deportation of mentally disordered offenders
Enhance arrangements to facilitate the return of prisoners earlier in their sentence
Asylum claims were now below 1997 levels, were being processed faster and failed asylum seekers sent back to their home countries.
Mr Cameron joked that Mr Blair would soon be blaming 19th Century Tory Prime Minister Sir Robert Peel for the problems.
He asked why, if minister Tony McNulty was judged too incompetent to run the immigration department, he had been put in charge of the police.
And pointing to the spate of Home Office problems, he said Mr Blair was one minister who had been in place for all of Labour's nine years in office.
He asked: "When is the prime minister going to take personal responsibility for this shambles?"
'Stop at nothing'
Mr Blair said he was happy to take responsibility for falls in overall crime, tougher sentencing and tackling anti-social behaviour.
He rejected the claims about Mr McNulty's move and said his minister had presided over more failed asylum seekers being removed.
Earlier, the home secretary pledged to "do whatever it takes to make the public feel safe" following a spate of Home Office.
He told the Daily Mirror he had set a deadline of 100 days to fix the system under which 1,019 foreign prisoners were not deported after their release.
Mr Reid said: "It can't be done in five minutes or five weeks. But I'll stop at nothing to make sure we get this right.
"I want to make the public feel safe again and I won't rest until the law and the justice system works for law-abiding people, not criminals."
Mr Reid added he wanted new Immigration Minister Liam Byrne to deliver a master plan in 100 days to prevent a repeat of the mistakes that allowed the foreign criminals to go free.