Speaking in Paris at a meeting with French President
"We have had these sorts of attacks before in our country, and we never buckle in the face of them," Cameron said.
According to unconfirmed reports, two assailants hit the victim with a car and then set upon him with various bladed weapons.
Officers rushed to the scene and found the victim, then shot the suspected attackers, who were taken to hospitals for treatment, said Cmdr. Simon Letchford of the Metropolitan Police Service.
The ITV television network said it had obtained video in which a man who may be one of the suspects speaks into a camera, holding knives in bloody hands and making statements that suggested he may have been motivated by Islamic militancy.
"We swear by almighty Allah we will never stop fighting you," the man says.
The lawmaker who represents the area where the attack occurred said the dead man was a soldier; Woolwich is home to barracks belonging to the Royal Artillery. But military officials have not confirmed this.
Cameron called the incident "shocking," and Home Secretary Theresa May was convening a meeting of the Cabinet's emergency committee, indicating high-level concern over the crime.