Michael Adebolajo, 28, is accused of hacking Fusilier Rigby to death with a meat cleaver and knives, along with Michael Adebowale, 22, on May 22 near Woolwich Barracks in south-east London.
During police interviews played to the jury at the Old Bailey, Abebolajo, covered by a blue blanket, said there was a "war between the Muslims and the British people" and he was a "soldier of Allah".
Asked what happened to Fusilier Rigby, Adebolajo said: "He was struck in the neck with a sharp implement and it was sawed until his head, you know, almost detached and may Allah forgive me if I acted in a way that is displeasing to him."
In an earlier interview, the murder suspect told officers the "leaders" of Britain were "wicked, corrupt, selfish and oppressive" and he was "particularly disgusted by David Cameron, the Miliband brothers and what's-his-name, Nick Clegg".
He added that people do not realise the "wickedness and corruption" of former prime minister Tony Blair.
Occasionally revealing his face to the camera's view, Adebolajo said: "It's for those people who have not yet understood the nature, the nature of the war that's ongoing and has been ongoing for some many years between the Muslims and the British people."
Adebolajo and Adebowale both deny murder, as well as attempted murder of a police officer and conspiracy to murder a police officer.
The trial was adjourned and is expected to resume today.