David Cameron insisted Britain would “never buckle” in the face of terrorist attacks as he led political condemnation of the soldier's murder, which he described as “absolutely sickening”.
The Prime Minister cut short a meeting with the French President, François Hollande, last night to return early to London and will chair a session of Whitehall's Cobra crisis committee this morning.
He told reporters in Paris: "There are strong indications it is a terrorist incident. Two people at the scene of the murder were wounded by the police and they are being treated as suspects."
He added: "The police and the security services in the UK will get all of the support they need to deal with this, or indeed with any other incident." He added that the country's thoughts would be with the victim and his family and friends.
"People across Britain... will utterly condemn this attack. We have had these sort of attacks before in our country and we never buckle in the face of them," he said.
Mr Cameron is expected to ask John Bercow, the Commons Speaker, to recall Parliament to give MPs an emergency statement on the attack. An initial session of the Cobra committee, bringing together ministers, police and the security services, was convened last night by Theresa May, the Home Secretary, who called the attack "sickening and barbaric".
The meeting is understood to have considered whether the two alleged attackers were acting alone or were part of a bigger network. Whitehall sources confirmed the murder was being treated as a terrorist incident.
Ms May was briefed on the attack by Sir Bernard Hogan-Howe, the Metropolitan Police Commissioner, and Andrew Parker, the head of MI5.
The Mayor of London, Boris Johnson, wrote on Twitter: "This afternoon's attack … is a sickening, deluded and unforgivable act of violence."
A spokesman for Ed Miliband said the Labour leader was cutting short a visit to Germany. He wrote on Twitter: "Shocked by appalling events in Woolwich. Whole country will be horrified."
A Buckingham Palace spokesman said the Queen would visit the King's Troop Royal Horse Artillery at Woolwich barracks, as planned, on 31 May.
Video: Man dies in Woolwich attack