David Cameron has insisted the UK will not be divided by the horrific murder of a serving British soldier on the streets of London.
The Prime Minister said the killing was "deeply shocking" and called it a betrayal of Islam as well as an attack on the British way of life.
The nation has been disgusted by the attack in broad daylight on Wednesday, which saw the soldier butchered by two men wielding cleavers.
But Mr Cameron cautioned against knee-jerk reactions to the murder and urged people to carry on with their normal lives.
In a passionate statement outside Number 10, he said: "What happened yesterday in Woolwich has sickened us all.
"The people who did this were trying to divide us. They should know something like this will only bring us closer together and make us stronger."
He added: "The country will be absolutely resolute in its stand against violent extremism and terror. We will never give in to terror - or terrorism - in any of its forms."
The Prime Minister called on Britons to come together and support the police and security services. "Confronting extremism is a job for us all," he said.
He hailed cub pack leader Ingrid Loyau-Kennett, who calmly challenged one of the attackers and was told that he wanted to start a war in London.
"She replied 'You're going to lose. It's only you versus many," he recounted, adding: "She spoke for us all."
Mr Cameron promised the police and security services would not rest until they had established every fact about the murder and its perpetrators.
Confirming the two suspects had been known to security services, he also said the police and intelligence response would be examined in due course.
He concluded: "The Police have responded with heightened security and activity - and that is right. But one of the best ways of defeating terrorism is to go about our normal lives and that is what we shall all do."
Security has been tightened at the Royal Artillery Barracks yards from the scene of the murder, and at other barracks across London.
Soldiers were also initially told not to wear uniform in public following the attack but this decision has now been reversed.
It has also been decided that the terror threat level for the UK - currently at substantial meaning an attack is a strong possibility - will not change.
Home Secretary Theresa May, Mayor of London Boris Johnson and Met Police chief Sir Bernard Hogan-Howe were among those at the Cobra summit on Thursday.
As he left Number 10, Mr Johnson appeared to indicate that the attack was a one-off and called for calm.
"Everything I am hearing leads me to think that Londoners can go about their business in the normal way and we are going to bring the killers to justice," he said.
Arriving for the summit, the Mayor had also expressed caution about connecting the murder to a particular faith or Government actions.
He said: "It is completely wrong to blame this killing on the religion of Islam but it is also equally wrong to try to draw any link between this murder and British foreign policy or the actions of British forces who are risking their lives abroad for the sake of freedom.
"The fault likes wholly and exclusively in the warped and deluded mindset of the people who did it. What we need now, for the sake of the victim and his family, is for those killers to be brought to justice."
For intelligence experts, the attack on a serving soldier in Britain is the realisation of one of their worst fears.
Since British forces arrived in Iraq and Afghanistan, troops have been aware they could be targeted at home by extremists.
British police have foiled at least two major plots in which Islamist suspects were accused of planning to kill off-duty troops.
Wednesday's attack is the first apparent Islamist killing in London since suicide bombers struck the transport system in July 2005.
The emergency response committee, which is called Cobra, first met on Wednesday after details of the horrific killing first emerged.
The meeting was called after eyewitness accounts indicated that the attackers had political and religious motives.
Tensions were heightened further amid signs of a backlash after more than 100 angry supporters of far-right group the English Defence League took to the streets.
Two men were also arrested in connection with separate attacks on mosques outside London, as anger and disgust spread across the country.
Intelligence experts will be frantically working to establish whether the attack was the work of so-called "lone wolves" or people with a more direct link to terror groups.
British counter-terrorism officials have recently warned that radicalised individuals who have no formal contact with al Qaeda are just as dangerous as those who do.
The two suspects, who were injured in the subsequent police shootout, are both British and believed to be of Nigerian descent, according to Sky sources.
Labour leader Ed Miliband cut short a trip to Germany because of the killing.
On Thursday, he said: "There are people who try to divide us with acts like this. They've tried it before in London and they've failed and they will always fail.
"There will be people who try to use events like this to divide us and they will fail too.
"British people are united across different faiths, different religions, different backgrounds, in their abhorrence of this and in values of decency and tolerance.
"That is the true character of the British people and that's why this terror will lose and will fail."
Security expert Simon Bennett said: "This would seem to be the first attack on a soldier in the UK motivated by some sort of Islamic fundamentalist agenda. In that sense, it's a new departure."
Peter Clarke, who led the investigation into the July 7 bombings, said if the Woolwich attackers did act alone, it showed the huge challenge facing the security services.
"An attack like this doesn't need sophisticated fund raising and sophisticated communications or planning. It can be organised and then actually delivered in a moment," he said.