The younger suspect, 22-year-old Michael Adebowale, was judged well enough to be released from the hospital and taken into police custody. Police said he is also suspected of attempted murder of a police officer.
The other suspect, Michael Adebolajo, 28, remains in a hospital in stable condition under armed guard. He was seen on a video boasting about the killing minutes after the attack. His family on Tuesday released a statement of condolence to Rigby's family, expressing horror and distress over the killing.
"Nothing we say can undo the events of last week," the statement read. "However, as a family, we wish to share with others our horror at the senseless killing of Lee Rigby and express our profound shame and distress that this has brought on our family."
Police have arrested a total 10 suspects including those shot at the scene in connection with last Wednesday's killing.
In Kenya, police said they believed Adebolajo, a British citizen, had earlier associated with a radical Kenyan Muslim cleric who tried to help him join an al-Qaida-linked rebel group in neighboring Somalia.
Muslim cleric Aboud Rogo Mohammed, who has since been killed, helped Adebolajo in his attempt to travel to Somalia to wage jihad, or holy war, against the country's United Nations-backed government, a senior Kenyan police official said Tuesday. The official insisted on anonymity because he is not authorized to speak to the press on this matter.
Adebolajo was arrested with five other young men in November 2010 in Kenya near the Somalia border and eventually returned to Britain.
Mohammed had been sanctioned by the U.S. Treasury Department for allegedly facilitating travel to Somalia for many young Kenyans wanting to join Somalia's al-Shabab rebels, who have launched terrorist attacks in and outside Somalia. The Treasury Department also charged that Mohammed was fundraising for al-Shabab.
In London, a worker for a rights group that lobbies on behalf of suspected terrorists said Adebolajo approached the group several months ago and appeared stressed and under pressure.
Arnaud Mafille, a case worker with advocacy group CagePrisoners, said Tuesday he believed Adebolajo was troubled by alleged abuse during detention in Kenya and "extreme harassment" by British security officials.
A friend of Adebolajo's alleged last week that agents from MI5, the U.K. domestic spy agency, tried to recruit him after he returned from Kenya. Kenyan officials have denied torturing Adebolajo.
The extensive revelations about Adebolajo's alleged attempts to link up with international terrorists have raised questions about whether Britain's intelligence services could have done more to prevent last week's killing. Britain's parliamentary intelligence committee said Tuesday it will investigate whether U.K. intelligence services fell short before the killing of Rigby.
British officials say the two main suspects had been known to them for some time as part of previous investigations.
With tensions high, Britain's counter-terrorism police were investigating a Sunday evening attack on two prison officers. Michael Spurr, chief executive of the National Offender Management Service, said in a statement that a prison officer was taken hostage for four hours by three Muslim prisoners at the Full Sutton prison in Yorkshire.
A second officer tried to aid the hostage, Spurr said. Both officers received hospital treatment.