Sir Denis O'Connor, outgoing HM Chief Inspector of Constabulary, will give evidence on Olympics security.
Stephen Greenhalgh, Deputy Mayor of London for Policing and Crime, will give evidence on policing in London.
Metropolitan Police Commissioner Bernard Hogan-Howe has also been asked to give oral evidence.
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Two-year-old Casper Platt-May and his six-year-old brother Corey died in the crash in Coventry on Thursday.
It means the petition, calling for a diverse panel to be appointed to the inquiry, has enough signatures to spark a debate in Parliament.
American businesses have begun severing ties with controversial pro-gun group the NRA in the wake of the latest mass school shooting.