UPDATE: The soldier killed in London’s Woolwich area on Wednesday was Lee Rigby, who held the rank of drummer, the Ministry of Defense said.
By Laura Smith-Spark
LONDON (CNN) -- Prime Minister David Cameron said Britain would be "absolutely resolute" in the face of terrorism Thursday, as he vowed that security services will not rest until they track down those responsible for the brutal hacking death of a British soldier in London.
Cameron condemned the "horrific attack" and said it had nothing to do with Islam, despite claims made by the two suspected attackers.
The thoughts of the country are with the victim and his family, he said.
Cameron spoke after a crisis meeting of senior officials, as security was increased at army bases around London amid fears of additional attacks.
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.
Cameron cut short an official visit to Paris to lead the summit, attended by Home Secretary Theresa May, Defense Secretary Philip Hammond, London Mayor Boris Johnson and senior police and security officials.
"We will never give in to terror or terrorism in any form," Cameron said.
Police searched an address in Lincolnshire, eastern England, in connection with the slaying, which took place in southeast London's Woolwich neighborhood.
Meanwhile, Assistant Commissioner Simon Byrne, of the Metropolitan Police, appealed for Londoners to remain calm, despite their shock, as investigations continue.
"London is at its best when we all come together, and now is the time to do that," he said.
Both men suspected in the attack were shot by police and are under guard at local hospitals. Authorities have not released their identities.
British media outlets including Sky and the Daily Mail are naming one of the suspects as Michael Adebolajo. CNN has not independently confirmed the name.
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 the summer of 2005, when London's public transport network was targeted with coordinated bomb attacks.
The scene of the gruesome killing, close to the Royal Artillery Barracks in Woolwich, 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 on Thursday that he knew one of the men named on social media as carrying out the Woolwich knife attack.
Choudary said the suspect had attended demonstrations and a few lectures organized by Choudary's group Al-Muhajiroun.
Cameron said Britons would stand together to defeat the threat of violent extremism.
"This was not just an attack on Britain and on the British way of life, it was also a betrayal of Islam and of the Muslim communities who give so much to our country," he said.
"There is nothing in Islam that justifies this truly dreadful act. ... The fault lies solely with the sickening individuals who carried out this attack."
Britain is working with its international partners to protect against terrorism "that has taken more Muslim lives than any other religion," Cameron said.
'I had better start talking to him'
Residents on Thursday shared with CNN their shock that something like this could have happened in the working-class, multicultural area where they live and work.
Construction worker Victor Easdown, who heard the shots ring out as police took on 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 saw that one of the attackers had a gun, he alerted police and 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 appeared to stay calm in the moments immediately afterward, prompting London Mayor Boris Johnson to pay tribute to their "exemplary courage and bravery."
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 on 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," political and social commentator Mohammed Ansar 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 and a sense of perspective. What we don't need are knee-jerk 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. Police responded 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
Nick Raynsford, the member of Parliament for Woolwich, told CNN the soldier apparently had 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 parliament member 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 Irish Republican Army in 1974. Two people died in the bombing.
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.
The Metropolitan Police said its first officers were on the scene within nine minutes of the alert being raised. The firearms unit was there 14 minutes after the first call was made, the force said.
"There has been an increased police presence in Woolwich and the surrounding areas overnight, and this will continue for as long as it is needed," said Assistant Commissioner Byrne.
"There were small incidents of minor disorder in Woolwich" late Wednesday, he said, but police dealt with these without arrests or reports of injuries or damage.
CNN's Carol Jordan, Atika Shubert, Erin McLaughlin, Ed Payne and Nic Robertson contributed to this report.