Michael Adebolajo, 28, spent a second day in custody at a London police station today after being discharged from hospital yesterday.
He is also being held on suspicion of attempting to murder a police officer in relation to the attack in Woolwich on May 22.
His suspected accomplice, 22-year-old Michael Adebowale, has been charged with the soldier's murder and appeared before Westminster magistrates on Thursday.
Both Londoners of Nigerian descent, believed to be Islamist extremists, were shot and arrested at the scene of the killing and were being held under police guard at different London hospitals.
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Police investigating the Woolwich attack have also arrested a 42-year-old man in north London and a 46-year-old man in east London on suspicion of involvement in the supply of illegal firearms.
The total number of arrests made in connection with the attack stands at 12.
So far, six of those arrested have been bailed and two released without charge.
A far-right British National Party (BNP) march is expected in Westminster later after police asked that it be moved from Woolwich.
Faith Matters, an inter-faith organisation aimed at tackling extremism, said it had recorded 212 Islamophobic incidents since last Wednesday, up from between four and six per day.
Queen Elizabeth II also paid her respects to the fallen soldier during a royal visit to the barracks yesterday.