Michael Adebolajo was believed to have been preparing to train and fight with the al-Qaida-linked Somali militant group al-Shabab in 2010 when he was arrested with five others, Kenya's anti-terrorism police unit head Boniface Mwaniki told The Associated Press.
The revelations came as London's Metropolitan Police said specialist firearms officers arrested another man suspected of conspiring to murder 25-year-old soldier Lee Rigby. Police did not provide details about the suspect, only saying he is 22 years old.
The latest arrest followed the detainment in London late Saturday of three others, aged 21 to 28, also suspected in the case.
Rigby, who has served in Afghanistan, was run over and stabbed with knives in the Woolwich area in southeast London on Wednesday afternoon as he was walking near his barracks.
Adebolajo, 28, and Michael Adebowale, 22, are the main suspects in the killing and remained under armed guard in separate London hospitals after police shot them at the scene.
In Kenya, Mwaniki said that Adebolajo was deported after his arrest in 2010. However, Kenya's government spokesman said he was arrested under a different name, and taken to court before being handed to British authorities.
"Kenya's government arrested Michael Olemindis Ndemolajo. We handed him to British security agents in Kenya and he seems to have found his way to London and mutated to Michael Adebolajo," spokesman Muthui Kariuki said. "The Kenyan government cannot be held responsible for what happened to him after we handed him to British authorities."
Kariuki said Adebolajo was travelling on a British passport, but he could not confirm if it was authentic.
When asked about reports that British embassy officials were involved, a Foreign Office statement said: "We can confirm a British national was arrested in Kenya in 2010. The Foreign and Commonwealth Office provided consular assistance as normal for British nationals."
Rigby's grieving family visited the scene of his murder on Sunday, pausing for a few moments in reflection and laying flowers to join the hundreds of floral tributes already left at the nearby Woolwich Barracks by wellwishers.
The soldier's gruesome murder has horrified Britain, partly because it was captured by witnesses' cellphones. A video picked up by British media showed one of the suspects, with bloodied hands, making political statements and warning of more violence as the soldier lay on the ground behind him.
Hardline Muslim leaders have identified the man in the video as Adebolajo, an Islam convert who allegedly used to take part in London demonstrations organized by British radical group al-Muhajiroun. The group catapulted to notoriety after the Sept. 11 attacks by organizing an event to celebrate the airplane hijackers, and was banned in Britain in 2010.
More than 20 supporters of the group have been arrested over terrorism offences, including a foiled plot to blow up central London nightclub Ministry of Sound and a bomb attack on London's Territorial Army base.