A man has been murdered in London in what is understood to be a terrorist killing of a British soldier.
The prime minister has cancelled a trip to Paris to meet French president Francois Hollande to travel back to the UK.
As he returned, a Cobra meeting took place chaired by home secretary Theresa May and attended by London mayor Boris Johnson.
"It is the most appalling crime," Cameron said during a joint press conference with the French president.
"We are urgently seeking the full facts about this case but there are strong indications it is a terrorist incident."
He added: "We've had these sorts of attacks before in our country and we never buckle in the face of them.
"We show indomitable British spirit. The terrorists never win because they cannot defeat the values we hold dear."
Police were called to John Wilson Street, Woolwich, early this afternoon after a man was reported to have been assaulted by two others.
A number of weapons, including a machete and a firearm, are understood to have been involved in the attack.
Police officers arrived at the scene followed by firearms officers but the man was already dead at the scene.
The two men were shot by the police and taken to separate hospitals in the capital, where they are receiving treatment.
A Buckingham Palace spokesperson said the Queen was "concerned" about the reports and was being kept informed.
"The Labour party will offer the government our complete support in establishing the facts of what happened and ensuring that those responsible face the full force of British justice," Labour leader Ed Miliband said.
Reports suggest the killing was committed by Islamic terrorists.
Disturbing video released by ITV showed one man talking to the camera, his hands covered in blood and a weapon in one hand.
"In our land our women have to see the same. You people will never be safe," the man says.
"Remove your governments. They don't care about you."
It appears the men made no effort to attack any other bystanders during the time it took for the police to arrive - roughly half an hour.
Instead they encouraged members of the public to take photos of them and issued political statements about the war in Afghanistan.
Cub scout leader Ingrid Loyau-Kennett stopped to help the victim.
"He was not high, he was not on drugs, he was not an alcoholic or drunk, he was just distressed, upset," she told the Telegraph.
"He was in full control of his decisions and ready to everything he wanted to do.
"I said 'right now it is only you versus many people, you are going to lose, what would you like to do?’ and he said 'I would like to stay and fight'."
In the evening a group of roughly 100 English Defence League (EDL) supporters gathered in the area and engaged in pitched battles with the police.
A Muslim Council of Britain statement said: "This is a truly barbaric act that has no basis in Islam and we condemn this unreservedly. Our thoughts are with the victim and his family.
"We understand the victim is a serving member of the armed forces. Muslims have long served in this country’s armed forces, proudly and with honour. This attack on a member of the armed forces is dishonourable, and no cause justifies this murder."
In a statement, Metropolitan police commander Simon Letchford said: "I can understand that this incident will cause community concerns, and I would like to reiterate that we are investigating what has taken place today.
"There will continue to be an increased police presence in this area, and the surrounding areas this evening. That presence will continue as long as is needed.
"I am asking people to remain calm, and avoid unnecessary speculation."