Prime Minister David Cameron vowed that Britain would not be cowed by the horrific bloodshed, and that it would reject "the poisonous narrative of extremism on which this violence feeds." In Washington, President Barack Obama said the U.S. "stands resolute with the United Kingdom" in the fight against violent extremism.
There were few signs of alarm on the streets of London, which has been hit by terrorist attacks during a long confrontation with the Irish Republican Army and more recently, in July 2005, by al-Qaida-inspired suicide bombings that killed 52 commuters.
"It's hateful, it's horrific and upsetting. But it doesn't seem to have made much of a difference," Christian White, 43, said at King's Cross station, close to the site of one of the 2005 bombings. "Londoners are used to living in a city where life is complicated."
Even so, security was increased at military barracks and installations in the capital, with extra armed guards added in many cases. Police said extra patrols were added at sensitive areas, including places of worship, transport hubs and congested areas.
Both of the hospitalized suspects had been part of previous terrorism investigations by Britain's security services, according to a British official who spoke on condition of anonymity because he was not authorized to speak about the police inquiry and cautioned that details could jeopardize future trials.
It was unclear how recent the investigations were, whether the men were loosely tied to other suspects being investigated, or whether they themselves had been put under surveillance, which could have included being watched by undercover investigators or having their phone calls and emails intercepted.
Dramatic video showed a black man — animated, hands stained with blood and holding a meat cleaver — criticizing the British government and the presence of U.K. troops in foreign lands.
Maajid Nawaz, a former Islamist now with the London-based Quilliam anti-extremism think tank in London, said the video and emerging details indicated the men had been inspired by al-Qaida even though they may not have been directed by any specific affiliate to attack the soldier.
"There is always mood music playing before these attacks happen," Nawaz told the AP. "In this instance, I'm not saying they are operationally linked to al-Qaida, but these men clearly felt an affinity to this global jihadist zeitgeist. And they wouldn't have had to have visited any foreign countries for this ideology to have resonated with them."
Security officials have been worried over the recent increase of men seeking training and fighting opportunities in countries such as Syria, Somalia and Yemen.
Dozens of British men and women are said to have been radicalized by U.S.-born militant cleric Anwar al-Awlaki, the militant leader who was killed in a 2011 U.S. drone strike in Yemen.
A Twitter account used by members of Somalia's al-Shabab militant group made a lengthy post Thursday about the attack in Woolwich.
The Twitter account referenced a video of the bloodied suspect calling the attack "an eye for an eye" for what it called the British army's "woeful record of abuses" against Muslims worldwide.
"We swear by almighty Allah we will never stop fighting you," the man in the video declared, complaining about British troops fighting Muslims. "We must fight them as they fight us."
The camera then panned away to show a body lying on the ground. This video, with its venomous threats, may provide the lasting image of the tragedy.
Police in the eastern England county of Lincolnshire said a property was searched in connection to the Woolwich attack. Police said a search warrant had been obtained but would not provide details. Police were also scouring the attack site for further clues.
There also was a police raid on a public housing complex in east Greenwich just outside of London thought to be related to the investigation.
One man was arrested Wednesday outside a mosque in Essex after he threw a smoke bomb, police said. He was also found to be carrying knives and is expected in court Friday. No one was injured.
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