The brutal terrorist murder of a "brave soldier" on the streets of London will bring the UK together and "make us stronger", David Cameron declared.
Speaking outside Downing Street after chairing a meeting of the Government's emergency Cobra committee, the Prime Minister said the attack "sickens us all" and was a "betrayal of Islam".
"The people who did this were trying to divide us. They should know something like this will only bring us together and make us stronger," he said.
"This 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.
"This view is shared by every community in our country. This was not just an attack on Britain and on the British way of life; it was also a betrayal of Islam and of the Muslim communities who give so much to our country.
"There is nothing in Islam that justifies this truly dreadful act."
He said the best response was for everyone to "go about our normal lives"
Mr Cameron cut short an official visit to Paris last night to return to the UK to co-ordinate the Government's response.
Speaking after meeting with police and intelligence chiefs, he said: "What happened yesterday in Woolwich has sickened us all. On our televisions last night and in our newspapers this morning, we have all seen images that are deeply shocking.
"Our thoughts are with the victim and with his family. They are grieving for their loved one and we have lost a brave soldier."
Mr Cameron cautioned against "knee-jerk responses" to the outrage.
Troops in London were advised in the immediate aftermath of the attack not to wear their uniforms outside their bases.
But the Cobra meeting agreed that issuing orders against wearing military uniforms in public would not be the right response.
"After an event like this it is natural that questions will be asked about what additional steps can be taken to keep us safe," Mr Cameron said.
"I will make sure those questions are asked and answered but I am not in favour of knee-jerk responses.
"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."
Mr Cameron said he could not comment on reports that the two men were known to the security services.
"The point that the two suspects in this horrific attack were known to the security services has been widely reported, you would not expect me to comment on this when a criminal investigation is ongoing.
"But what I can say is this, as is the normal practice in these sorts of cases the Independent Police Complaints Commission will be able to review the actions of the police and the Intelligence and Security Committee will be able to do the same for the wider agencies.
"But nothing should be done to get in the way of their absolutely vital work."
The police and security services will not stop until "every single detail" of what happened is clear, Mr Cameron said.
"The police and security services will follow every lead, will turn over every piece of evidence, will make every connection and will not rest until we know every single detail of what happened and we have brought all of those responsible to justice.
"I know from three years of being Prime Minister that the police and intelligence services work around the clock to keep us safe from violent extremists.
"I watch their work every week, they do an outstanding job.
"They show incredible heroism, much of which cannot be reported.
"They have my staunch support and the support of the whole country."
He hailed the bravery of Ingrid Loyau-Kennett, who confronted one of the killers, saying she "spoke for us all".
"Confronting extremism is a job for us all. And the fact that our communities will unite in doing this was vividly demonstrated by the brave Cub pack leader Ingrid Loyau-Kennett, who confronted one of the attackers on the streets of Woolwich yesterday afternoon.
"When told by the attacker he wanted to start a war in London she replied you're going to lose, it is only you versus many.
"She spoke for us all."