One of soldier Lee Rigby's suspected killers was being questioned by police as protest marches were due to begin around the country.
Michael Adebolajo, who was shot by police, was released from hospital on Friday and taken into custody.
The 28-year-old had already been arrested on suspicion of Drummer Rigby's murder, and was further arrested on suspicion of the attempted murder of a police officer.
Michael Adebowale, 22, has already been charged with murdering the young soldier and is due to appear at the Old Bailey on Monday.
Meanwhile, two men aged 42 and 46 arrested on suspicion of being involved in the illegal supply of guns were bailed today to return to a south London police station later this month.
Far-right and opposing groups are holding demonstrations amid increased tensions following the violent death of 25-year-old Drummer Rigby.
In a statement released through the Ministry of Defence, members of Drummer Rigby's family including his mother Lyn, stepfather Ian, wife Rebecca and son Jack, said: "We would like to emphasise that Lee would not want people to use his name as an excuse to carry out attacks against others.
"We would not wish any other families to go through this harrowing experience and appeal to everyone to keep calm and show their respect in a peaceful manner."
On Saturday, the British National Party is holding a march and motorcade in Westminster.
The far-right party had originally planned to march in Woolwich, south east London, but police stepped in to stop this to avoid igniting community tensions.
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