After chairing an emergency meeting of the high-level COBRA crisis group, Cameron said Britain's communities would unite in condemning yesterday's attack which he described as a "betrayal of Islam".
Cameron, who cut short his visit to Paris, said the terror attack was "deeply shocking" that has "sickened us all".
"What happened yesterday in Woolwich has sickened us all. We have lost a brave soldier," Cameron said, addressing the media outside 10 Downing Street.
"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...Confronting extremism is a job for us all," he added.
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Anti-terror police forced their way into a flat and shattered the door frame as they raided an address believed to belong to one of the attackers on a Greenwich housing estate.
They also raided an address in Saxilby, Lincolnshire, in connection with the attack.
"This is in connection with the ongoing investigation into the murder of a man in Woolwich. The Metropolitan Police are not prepared to discuss the matter further at this stage," they said.
Both suspects in the killing were known to security services, senior Whitehall sources have said.
One of the suspects is understood to be 28-year-old Muslim convert Michael Adebolajo, who is believed to be a British citizen of Nigerian descent, according to sources.
He and another man were under arrest in hospital after being shot by police following yesterday's attack in Woolwich.