Labour election chief Alan Milburn has apologised for the death of a policeman killed by ricin plotter Kamel Bourgass.
Kamel Bourgass had failed to get asylum
Bourgass has been jailed for life for the murder of DC Stephen Oake. The Conservatives say he was only in the UK because of a "chaotic" asylum system.
Home Secretary Charles Clarke said the government had accepted responsibility. But he said things had improved and urged the Tories to support ID cards.
The Lib Dems oppose ID cards but want a border security force and more police.
Bourgass, who had at least four false identities, has been jailed for murder and plotting to spread poisons.
Bourgass said he had entered the UK in 2000 using forged documents. His asylum claim was rejected in 2001 but he was not arrested until January 2003, when he killed DC Oake.
Asked if he would apologise for asylum failures which allowed Bourgass to stay in the UK, Mr Milburn said: "What we apologise for is the death of that police officer serving his country, trying to protect his country."
The issue now was how to prevent such incidents happening again, he added.
Labour also stresses that only Bourgass is responsible for Dc Oake's murder.
Legislation to introduce identity cards was dropped just before the election - something the government blames on Conservative and Liberal Democrat opposition.
Mr Milburn said ID cards would be a priority of the first Queen's speech after the election if Labour won the election.
Challenging the Conservatives to support the cards, he said: "There is no scope for playing politics on this."
The Tories say the ID card plans would not apply to failed asylum seekers like Bourgass.
Since 2002, asylum seekers have been issued with Application Registration Cards (ARC), which contain a photograph and fingerprints.
Under the Home Office's five-year plan, this would become a full biometric identity card which would have to be produced by anyone entering the country for more than three months.
After Mr Milburn's comments, Conservative leader Michael Howard said: "He was right to apologise.
"Of course that involves acceptance of the responsibility of the government for what happened.
"Truth is that Britain's asylum system is in chaos. That is not something I have been saying today or yesterday but something I have been saying for months and years."
Home Secretary Charles Clarke said stronger border controls at the time could have inhibited the terrorist threat.
"Of course, the government has to take responsibility," he said.
But Mr Clarke also told BBC News: "We have made major advances.
"Asylum applications are reduced by two-thirds since 2002, removals are three-quarters higher than in 1997 but... there are a whole series of further measures we need to take to address it."
Mr Clarke also stressed asylum seeking should not be confused with terrorism.
The Liberal Democrats have accused the Tories of exploiting the issue and say the ricin case must not be used to cast a "slur" on all asylum seekers.
The party opposes ID cards, saying they would not stop determined terrorists.
Lib Dem chairman Matthew Taylor said: "We need a national border security police force, we need 10,000 more police, we need more resources for the Home Office for investigation and detection."