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 the video in which the bloodied suspect called the attack "an eye for an eye." The tweet said the British army had a "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.
Separately, police in Kent said they charged a 45-year-old man with religiously aggravated criminal damage and burglary. The man, Andrew John Grindlay, was arrested Wednesday night.
There were no incidents reported at London mosques. Police called for calm and said there were 1,200 officers deployed on the streets.
Britain's security threat remained the same since the killing, but security officials said they were reviewing preparations for the June 17-18 Group of Eight summit in Northern Ireland. Obama and other world leaders are expected to attend.
Police defended the speed of the department's response to the Woolwich attack. Assistant Commissioner Simon Byrne said police were on the scene nine minutes after receiving the first emergency call. Once it became clear that guns were involved, firearms officers were called and arrived 14 minutes after the first call to police, he said.
The Ministry of Defense said Rigby, who joined the army in 2006, was a machine gunner posted in Cyprus, Afghanistan and Germany before becoming a recruiter who assisted with duties in the Tower of London.
Nicknamed "Riggers," he was an important member of the Corps of Drums who was known for his good nature and wit, and his love of his hometown soccer team, Manchester United, according to fellow soldiers.
"He was one of the battalion's great characters, always smiling and always ready to brighten the mood with his fellow Fusiliers. He was easily identified ... on parade by the huge smile on his face and how proud he was to be a member of the Drums," Warrant Officer Class 1 Ned Miller said in a statement issued by the ministry.
Rigby's family said he would "do anything for anybody," always looked out for his sisters and took a "big brother" role with everyone he met.
"He was a loving son, husband, father, brother, and uncle, and a friend to many," the family said in a statement issued by the ministry.
Associated Press writers Cassandra Vinograd, Sylvia Hui, Matt Surman and Danica Kirka in London and Zeina Karam in Beirut contributed to this report.