Abedi detonated a bomb on 22 May at the end of a concert by US singer Ariana Grande.
MI5 said it would hold an inquiry into the way it dealt with warnings from the public that he was a potential threat.
The security service, which was alerted to his extremist views three times prior to last Monday’s attack, will examine how it dealt with the warnings.
Home Secretary Amber Rudd said it was right for MI5 to review its processes.
MI5 has launched a “post incident investigation” into how the Manchester bomber was overlooked, while a separate report is being prepared for ministers and those who oversee the work of the service.
A Whitehall official said previously that Abedi was one of a “pool” of former subjects of interest whose risk remained “subject to review” by the security service and its partners.
Born in Manchester to Libyan parents, BBC Newsnight reported that when Abedi was 16 he fought against the Colonel Gaddafi regime with his father during the school holidays.
It was while at Manchester College that two people who knew Abedi have confirmed they made separate calls to an anti-terrorism hotline to warn the police about his extremist views.
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