Islamist connections claimed
Adebolajo had been a follower of Al-Muhajiroun, a British group of Islamic extremists virulently opposed to UK intervention in Iraq and openly supportive of al Qaeda, according to several Al-Muhajiroun insiders.
He attended meetings of the group in London, they said, before moving away from the group two or three years ago.
Details about his purported connections to Somalia's Al-Shabaab movement are unclear.
The Islamist militants control much of southern Somalia and have long been affiliated with al Qaeda.
In 2011, Kenya sent forces to the neighboring nation to battle Al-Shabaab, which it blamed for kidnapping foreigners and launching grenade and gun attacks in Kenya.
Kariuki, the Kenyan government spokesman, said that Adebolajo was arrested in the coastal town of Lamu in 2010 and released to British security officials inside Kenya. No charges were filed against Adebolajo, according to the Kenyan media.
Lamu is part of an area near the Somali border that has been the stage for attacks by armed gangs and suspected operatives from Al-Shabaab.
On Sunday, one Kenyan official pointed to the 2010 arrest of Adebolajo and other British nationals as a sign that his country's approach fighting terrorism was working.
"On (the) war against terrorism, Kenya security forces have been ahead of the curve," said Bitange Ndemo, who heads Kenya's information ministry. "In 2010 our security forces arrested a number of British nationals on suspicion of terrorism activities. Relevant British authorities in Kenya were contacted. This action reaffirms Kenya's position as a credible and highly effective player in the fight against terror and organized crime."