Many are asking why more wasn't done to prevent the shootings after a spate of antisemitism-related offences.
The 78-year-old UK citizen was convicted of lobbying foreign governments to impose sanctions on HK and China.
Authorities say two rabbis, a Holocaust survivor and a 10-year-old girl were among the victims.
He directed classic films including The Princess Bride, This is Spinal Tap and When Harry Met Sally.
Two people died and nine others were injured in the incident in Rhode Island on Saturday.
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