To carry out a full investigation, involving hearing sensitive material in private, would require a public inquiry, which can hold some of the hearings behind closed doors with press and public excluded.
Judge Durran made the decision to ask for a public inquiry be established following the pre-inquest hearing on 4 September.
At the hearing, lawyers for the government said if the MI5 material was released, it would harm national security.
Lawyers for the families of the two victims questioned why private hearings were necessary for the disclosure of MI5 material, as the authorities had stated publicly that Al-Shamie was not known to security services.
Al-Shamie launched his attack on 2 October last year by driving into the perimeter gates of the synagogue then attacking worshippers with a knife while wearing a fake suicide belt.
Cravitz died from multiple knife wounds, while Daulby was killed by a bullet fired by armed officers who had been scrambled to the scene.
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