Theresa May is under increasing pressure over a former Guantanamo Bay inmate who received a reported £1million payout and went on to become an Islamic State suicide bomber.
He was released from the American holding centre on the eastern tip of Cuba in 2004, while Tony Blair was still Prime Minister.
But the former prime minister said that the lucrative payment was signed off by the Conservative-led coalition government six years later.
And ex-Home Secretary Lord Blunkett said that monitoring of ex-Guantanamo Bay detainees stopped in 2010, when Mrs May was the Home Secretary.
The bomber, who has been named by IS as Abu Zakariya al-Britani, is reported to have died as he detonated a vehicle filled with explosives south of Mosul in Iraq.
He has been identified as Muslim convert called Ronald Fiddler, also known as Jamal Udeen.
Mr Blair said: "When his release was announced in very measured terms in 2004, pointing out the risks which remained with Guantanamo detainees, ...Conservative MPs reacted by strongly criticising not the release, but why it had taken so long.
"The fact is that this was always a very difficult situation where any Government would have to balance proper concern for civil liberties with desire to protect our security, and we were likely to be attacked whatever course we took.
"The reason it did take a long time for their release was precisely the anxiety over their true affiliations.
"But those who demanded their release should not be allowed to get away with now telling us that it is a scandal that it happened."
The payout was agreed in 2010, the former Labour leader said.
A Downing Street spokesman declined to answer questions on the payment, saying it was an intelligence matter.
Last night No 10 suggested that the dead man might not be Fiddler.
Fiddler's family played down suggestions that he had received as much as £1 million.
Terror experts defended the money, saying it had been necessary to protect key sources from being revealed in court.
A Labour source said that detention camps like Guantanamo had been a major recruiting sergeant for Islamist terror groups.
But former Labour Home Secretary Jack Straw said a government led by his party might also have paid out.
He said: "The difficulty at that time was that there was no mechanism by which the evidence against these people who were suing the British government for complicity could be taken into court without the risk of us disclosing really sensitive intelligence which could, in turn, literally have led to the death of British agents."
The law has since been changed.
Meanwhile, Mrs May attempted to head off backbench anger over business rate rises in England.
Communities Secretary Sajid Javid told MPs that the Conservative Government would announce measures in next month's Budget “to provide further support to businesses facing the steepest increases".
A No 10 spokesman said: "We would never confirm or deny what would be in the Budget this far in advance."
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