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Mr Clarke also said that anti-terror legislation, which was formulated before the London bombings, would be brought forward as soon as is practicable after Parliament returns in October. He said he hoped to proceed "by means of consensus".
At the heart of the forthcoming Counter-Terrorism Bill will be three new criminal offences: acts preparatory to terrorism; indirect incitement to terrorism - which will cover those who glorify and condone terrorist acts; and giving and receiving terrorist training.
"There is unity of purpose. The Government wants to work with other parties to make sure we have the most effective anti-terrorism legislation on our statute book," he said. "Similarly we want to work with the Muslim community to isolate and weaken dangerous extremists.
"We are all determined to take whatever steps are needed to identify, track down and bring to justice all those involved in instigating, planning, supporting these terrible crimes."
The Government is also concluding a series of agreements allowing it to deport terror suspects to their home countries, where previously they might have been expected to face cruel or inhuman treatment, or even the death penalty.
It emerged today that the first agreement in principle has now been struck with Jordan, and could see the deportation there of Abu Qatada, one of the group of foreign terror suspects held for more than two years at Belmarsh prison.
Abu Qatada is now under a control order limiting his movements and activities. He is a Jordanian-Palestinian preacher, sometimes described as Osama bin Laden's "ambassador in Europe", who has been convicted in absentia in Jordan for bomb plots there. Other agreements are being negotiated, especially with North African nations.
Announcing the possible international conference on terrorism, Mr Blair said around 26 countries had suffered from al-Qaeda and its associated networks since 1993.
He said: "There is obviously a huge well of support and understanding for the problems we have faced in this country recently. But we have to be very clear about this: though the terrorists will use all sorts of issues to justify what they do, the roots of it do go deep; they are often not to be found in this country alone. Therefore, international action is also necessary."
Mr Clarke said that 56 people are known to have died in the London bombings, all of whom have now been formally identified.
He said that the death toll could yet rise as the police investigation of the crime scenes continues - especially from the bomb blast on the Piccadilly Line between King's Cross and Russell Square. Twenty-seven people are still being treated in hospital.
Mr Clarke said that, following the removal of the bombed train, Aldgate Station should reopen by Monday and it was hoped to restore full services on the Circle Line, interrupted by the Edgware Road blast, within a couple of weeks.
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