LONDON (CNN) -- Prime Minister David Cameron called a meeting of Britain's civil emergency committee on Thursday, looking for answers in the aftermath of the daylight hacking death of a British soldier in London.
The meeting comes as security was increased at army bases around London amid fears that additional attacks could be possible.
The calling of the crisis meeting Thursday -- the second in less than 24 hours -- indicates how seriously the government is taking what it believes is a terrorist incident. Home Secretary Theresa May, Defence Secretary Philip Hammond, London Mayor Boris Johnson and senior police and security officials all attended.
Chief among the questions was likely who the two attackers are and whether they form part of a wider terror cell.
Both men suspected in the attack were shot by police and are under guard at local hospitals. Their identities have not been released by authorities.
The victim was a serving soldier, London's Metropolitan Police said. They are not releasing his name in line with his family's wishes.
The capital has not witnessed an alert of this kind since summer 2005.
"We will never buckle under these sorts of attacks," Cameron said Wednesday. "The terrorists will never win."
The scene of the gruesome killing, close to the Royal Artillery Barracks in southeast London's Woolwich neighborhood, remained cordoned off as police searched the scene Thursday morning.
A video recorded by one of the two men immediately after the attack seemed to suggest a jihadist agenda.
"We swear by almighty Allah we will never stop fighting you until you leave us alone," said a meat-cleaver-wielding man with bloody hands, speaking in what seems to be a London accent.
"The only reasons we killed this man ... is because Muslims are dying daily," he added, in video aired by CNN affiliate ITN. "This British soldier is an eye for an eye, a tooth for tooth."
British soldiers have participated in the wars in Afghanistan and Iraq.
Prominent British Muslim radical leader Anjem Choudary told CNN Thursday that he knew one of the men named on social media as carrying out the Woolwich knife attack.
Choudary claimed that the suspect had attended demonstrations and a few lectures organized by Choudary's group Al-Muhajiroun.
'I had better start talking to him'
Residents shared with CNN Thursday their shock that something like this could have happened where they live and work.
Construction worker Victor Easdown, who heard the shots ring out as police tackled the attackers, fears the incident could fuel tensions and reprisal attacks.
"People can only take so much. And people will break," he said.
Graham Wilder, a resident whose son attends a nearby school, told how he feared for the safety of his family and other children who had just left the school Wednesday afternoon.
After he spotted one of the attackers had a gun, he alerted police and the school authorities, Wilder said. He heard shots fired and screamed for his wife, who was at a nearby store, to get down.
But despite the savagery of the attack, eyewitnesses in Woolwich, a working class area with a multicultural community, appeared to stay calm in the moments immediately afterward.
Video footage showed passersby gathered nearby, and one woman, Cub scout leader Ingrid Loyau-Kennett, told Britain's Daily Telegraph newspaper how she tried to talk to the two attackers to stop further violence.
The mother-of-two had jumped off a bus after seeing the man on the ground to see if she could give him emergency aid, she told the newspaper.
But she swiftly realized the man was dead, and it was not an accident.
"When I went up there was this black guy with a revolver and a kitchen knife, he had what looked like butcher's tools and he had a little axe, to cut the bones, and two large knives and he said, 'Move off the body'.
"So I thought 'OK, I don't know what is going on here' and he was covered with blood. I thought I had better start talking to him before he starts attacking somebody else."
Another witness, Michael Atlee, described the gruesome, frenzied and ultimately fatal sequence of events as "a bloody mess." The men first ran the victim down in a car before attacking him with knives, he said.
'They were just animals'
A man who identified himself as James told London's LBC 97.3 radio station that he saw two men standing by the victim, who was on the ground.
At first James thought they were trying to help the man. But then he saw two meat cleavers, like a butcher would have.
"They were hacking at this poor guy, literally," he told the radio station. "These two guys were crazed. They were just not there. They were just animals."
The brazenness of the attack, along with the fact that the men waited some 30 minutes for police to arrive without trying to flee, seemed to indicate they wanted to publicize their message.
The men appeared to want to be filmed, with one of the attackers going over to a bus and asking people to take photos
of him as if he wanted to be on TV.
A man who asked not to be identified told ITN that he was on his way to a job interview when he came up on the scene and started filming it. Then, a man with a cleaver and knife in his bloody hands "came straight to me (and) said, 'No, no, no, it's cool. I just want to talk to you.'"
The suspect went to apologize to women who had witnessed the attack, then quickly added "but in our lands our women have to see the same."
"You people will never be safe," he said. "Remove your government. They don't care about you. You think David Cameron is going to get caught in the street when we start busting our guns?
"... Get rid of them. Tell them to bring our troops back so we can all live in peace."
There were concerns the brutal incident might inflame animosity against Muslims, with Metropolitan Police deploying riot police as a precautionary measure.
The Muslim Council of Britain, after condemning what it called "a truly barbaric act that has no basis in Islam," urged Muslims and non-Muslims alike "to come together in solidarity to ensure the forces of hatred do not prevail."
"What we have seen on the streets of London has been particularly sickening, a really, really heinous act of I would say criminality -- and I'm being careful to say criminality, not terrorism," Mohammed Ansar of the council told CNN.
The motivation behind what happened remains unclear, he pointed out.
"What we need at this time is a sense of calm, a sense of measure nad a sense of perspective. What we don't need are kneejerk reactions ... to really ratchet up tensions and really stoke and inflame anxieties within communities."
Members of the far-right English Defense League clashed with police late Wednesday.
The group's official Twitter account posted this call to action: "ANY EDL MEMBERS TAKE TO THE STREETS IN YOUR LOCAL TOWN/CITY TAKE A STAND !!!!!!"
Later Wednesday, a man with two knives threw a smoke grenade into a mosque in Essex, a county east of London, and demanded someone come outside to answer to the Woolwich slaying, the mosque's secretary said. The only person inside called police who came quickly and arrested the man, said Al Falah Braintree Islamic Center secretary Sikander Sleemy.
"I believe this was a revenge attack for what happened in Woolwich," Sleemy said. "We strongly condemn what happened in Woolwich. It's not an Islamic act."
In Kent, police arrested a man on suspicion of "racially aggravated criminal damage" at a religious building.
Soldiers targeted before
Cameron -- who was in France at the time of the incident but headed back home promptly -- declined to confirm if the man killed was a serving soldier, while Britain's Defense Ministry said it was investigating to see whether that's the case.
But Nick Raynsford, the member of Parliament for Woolwich, told CNN that the victim is believed to be a serving soldier who had apparently been on duty in central London and was returning to the barracks when he was attacked.
Troops stationed at the historic military barracks have a close relationship with locals, the MP said.
This isn't the first time British soldiers have been singled out.
Last month, four radical Islamists were convicted at Woolwich Crown Court of a plot to drive a car full of explosives, by remote control, into an army barracks in Luton, north of London.
Several years earlier, police interrupted a a scheme in which Islamists planned to kidnap a solider of Pakistani heritage and behead him. Their plan called for releasing an Internet video of the decapitation.
A pub in the same area of Woolwich was targeted by the IRA in 1974. Two people died in the bombing.
Letchworth said both suspects were taken to separate London hospitals for treatment. Metropolitan Police Commissioner Bernard Hogan-Howe later said the two had been arrested, though it wasn't immediately clear if this happened at the hospitals or elsewhere.
"We understand concern about the motivation, and we will work tirelessly to uncover why this occurred and and who was responsible," Hogan-Howe said. "I understand people want answers, but I must stress we are in the early stages of investigations."
Local residents said police responded quickly when the alarm was raised Wednesday afternoon but questioned how long it had taken for a specialist firearms unit to arrive. British police typically don't carry guns.
Defense Minister Hammond said the killing was a "very shocking incident" and that the United Kingdom takes the safety of its troops "very seriously."
The attack spurred other swift condemnations around the world and especially in Britain -- from a "concerned" Queen Elizabeth II, to London Mayor Boris Johnson's description of a "sickening and unforgivable act of violence," to Labour Party leader Ed Miliband's prediction that the "whole country will be horrified."
CNN's Carol Jordan, Atika Shubert, Erin McLaughlin, Ed Payne and Nic Robertson contributed
to this report.
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