"Some of them are quite aggressive, very focused, very aggressive attacks ... against institutions or places where Muslims congregate," he said.
Questions abound over what could have led the two men to attack Rigby, a drummer and machine-gunner who had served in Afghanistan and was off-duty when he was walking near his barracks. Nusaybah's interview with the BBC offered one possible narrative. He said Adebolajo became withdrawn after he allegedly suffered abuse by Kenyan security forces during interrogation in prison there.
"Although that change wasn't necessarily one that became overt, aggressive or anything like that, he became ... less talkative. He wasn't his bubbly self," Nusaybah told the BBC.
He said MI5 agents approached Adebolajo after he returned to Britain and initially asked him if he had met specific Muslim militants, then asked Adebolajo if he was willing to act as an informer.
"He was explicit in that he refused to work for them," Nusaybah said.
The BBC said police arrested Nusaybah outside its studio immediately after the interview was recorded.
"This interviewee had important background information that sheds light on this horrific event," the BBC said in a statement. "And when we asked him to appear and interviewed him, we were not aware he was wanted for questioning by the police."
It was not immediately possible to verify the information provided by Nusaybah, who said he had known Adebolajo for about a decade. MI5 does not publicly discuss its efforts to recruit informers.
In Kenya, Anti-Terrorism Police Unit chief Boniface Mwaniki said police were checking their records to confirm whether Adebolajo had been in their custody. Mwaniki rejected any suggestion that Adebolajo had been abused.
Nusaybah said Adebolajo converted to Islam around 2004. His account corroborates those provided by two Muslim hard-liners who said they also knew Adebolajo.