Britain will "never buckle" in the face of terrorist incidents, David Cameron vowed, as he condemned the "absolutely sickening" killing in London.
"Tonight, our thoughts should be with the victim, with their family, with their friends," the Prime Minister said.
"People across Britain, people in every community, I believe, will utterly condemn this attack.
"We have had these sorts of attacks before in our country and we never buckle in the face of them."
Mr Cameron was speaking at a Paris press conference with French president Francois Hollande but confirmed he would cut short the visit to return to the UK tonight to chair a meeting of the Government's Cobra emergency committee in the morning.
"I have been briefed by the Home Secretary about this absolutely sickening attack.
"It is the most appalling crime. We are obviously seeking, and the police are urgently seeking the full facts about this case, but there are strong indications that it is a terrorist incident."
Mr Cameron said: "We will look at every aspect of security, we will look at every aspect of what you can learn from these incidents.
"But we also have to remember that in a free country like ours, the best way to defeat terrorism is to make sure that you continue to go about your life, to live your life and show that terrorists can never win, and that's important."
President Hollande said he wanted to "express all of my solidarity to David Cameron and the United Kingdom after the murder of the British solider in London earlier today.
"We must fight terrorism everywhere. It requires that we share our intelligence, that our intelligence services work together and that we act everywhere we can."
He specifically highlighted the support given by the UK to France's military intervention in Mali.
Asked about Mr Hollande's comments, Mr Cameron declined to confirm that the victim was a serving soldier.
London and Paris were proud to "stand together in the fight against extremism, against violence and against terrorism", he said.
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