David Cameron says Britain has faced terror attacks such as the one in Woolwich before and has always beaten them back.
The Prime Minister was speaking at a news conference in Paris before cutting short the visit to return to the UK to chair a meeting of the Government's Cobra emergency committee this morning.
"I have been briefed by the Home Secretary about this absolutely sickening attack," Mr Cameron said.
"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.
"Tonight, our thoughts should be with the victim, with their family, with their friends."
Home Secretary Theresa May described it as "an attack on everyone in the United Kingdom" after a Cobra meeting on Wednesday evening.
"The police and Security Service are establishing the full facts of this barbaric case, but there is a strong indication that it was an act of terrorism," she said.
"The Prime Minister is returning to London and will chair another Cobra meeting in the morning.
"In the meantime, security has been increased at army barracks across London."
The Prime Minister said at the news conference that "terrorists will not win".
"We have suffered these attacks before and we have always beaten them back," he said.
"But above all the ways we've beaten them back is (by) showing an absolutely indomitable British spirit.
"That we will not be cowed (and) we will not buckle under these sorts of attacks.
"The terrorists will never win because they can never beat the values that we hold dear.
"The belief in freedom, in democracy, in free speech, in our British values, Western values.
"They are never going to defeat those, and that is how we will stand up to these people: whoever they are, however many there are of them.
"And that is why we will always win."
In expressing solidarity with Mr Cameron, French president Francois Hollande referred to the murdered man as a "British soldier", but Mr Cameron refused to confirm this.
Sky Home Affairs Correspondent Mark White said here has been a concern for some considerable time about the potential for homegrown terrorist groups.
"These kind of attacks do not need to be sophisticated and in many respects the less sophisticated they are, the more easily an attack can be perpetrated," he said.
"These homegrown terrorist cells of very low sophistication can choose insecure targets that do not have any level of security around them by going into crowded places or taking on individuals.
"The concern the police and the security services have is just how to keep an eye on these radicalised individuals who are willing to carry out low-level, unsophisticated attacks like this would seem to have been."