Tony Blair has vowed not to "give an inch to terrorism" and said Iraq was no excuse for the London bombings.
He acknowledged Iraq was being used to recruit terrorists, but insisted the roots of extremism were much deeper.
He said 11 September 2001 was a wake up call for the international community, but argued some people "then turned over and went back to sleep again".
The prime minister was speaking to reporters after talks about new terror laws with Tory and Lib Dem leaders.
He said: "Let us expose the obscenity of these people saying it is concern for Iraq that drives them to terrorism. If it is concern for Iraq then why are they driving a car bomb into the middle of a group of children and killing them?
"We are not going to deal with this problem, with the roots as deep as they are, until we confront these people at every single level - and not just their methods but their ideas," he added.
"11 September for me was a wake up call. Do you know what I think the problem is? That a lot of the world woke up for a short time and then turned over and went back to sleep again."
In a 75 minute media conference Mr Blair said there was no justification for suicide bombing whether in Israel or in "Palestine, Iraq, in London, in Egypt, in Turkey, anywhere. In the United States of America, there is no justification for it. Period".
Earlier, after the talks in Downing Street, Conservative leader Michael Howard said the prime minister was seriously considering allowing the use of "phone tap" evidence in courts.
Howard: Can see 'difficulties' with extending detention time
They also discussed extending the time suspects can be held without charge.
But he said the Tories saw extreme difficulties with calls from the police to extend the time a terrorist suspect can be held without charge from 14 days to three months.
Police chiefs say they only want to be able to ask a judge to ask to extend detentions in instalments up to the new time limit.
Mr Kennedy said "reasonable progress" had been made in the talks and he hoped this would continue in a measured way so "we don't surrender basic civil liberties in the process".
Downing Street has said Mr Blair still intends to listen to "considered advice" before supporting the use of telephone call recordings at trials.
There is already agreement on proposals to create new offences of engaging in acts preparatory to terrorism and of indirect incitement to terrorism.
WHO IS BEING HELD?
25 July - Second man arrested near Curtis House, north London
24 July - First man arrested near Curtis House
24 July - Man arrested in Tulse Hill, south London
22 July - Two men arrested in Stockwell, south London
Police meanwhile continue to hunt the men behind Thursday's failed bomb attacks on three London Underground trains and a bus.
They are holding five other men in connection with the attacks - but the five are not suspected of being bombers themselves.
On Tuesday officers found a large amount of "possible" explosives at a block of flats in New Southgate, north London, where bomb suspect Yasin Hassan Omar had been living since 1999.
The other bombing suspect named so far, Muktar Said Ibrahim, 27, has also been linked to the same flat.
TRACKS OF THE BOMB SUSPECTS
All journeys started between 12:20 and 12:25. Times approx.
OVAL: Man boards northbound Northern Line train at Stockwell and tries to set off bomb between Stockwell and Oval, where he leaves the train. He is chased out of the station at 1235 BST, but escapes towards Brixton.
HACKNEY: Man, identified by police as Muktar Said Ibrahim - or Muktar Mohammed Said - also sets off from Stockwell. Boards Number 26 bus at 1253 at Bank. Police believe he was carrying bomb in a grey and black rucksack, and tried to detonate bomb while on board. Gets off in Hackney Road, near junction with Colombia Road, at 1306.
WARREN STREET: Man who police believe is Yasin Hassan Omar boards Tube train at Stockwell carrying a purple rucksack that they say contained a bomb. Later tries to set off bomb on a northbound Victoria Line train between Oxford Circus and Warren Street, detectives say. Seen without rucksack at 1240 in Warren Street Station before running towards exit and vaulting over ticket barriers.
SHEPHERD'S BUSH: Man wearing dark blue baseball cap and carrying small rucksack enters Westbourne Park Tube station and gets a train travelling towards Shepherd's Bush on Hammersmith & City Line. Tries to set off bomb at 1225 before escaping, probably through window at the end of the carriage, and running along the tracks.