It is still unclear if the passport belonged to the terrorist or if he was himself a refugee.
Rabbi Mirvis said: “I am aware because of the possibility that one or more of the terrorists came though Greece in the guise of refugees there has been a suggestion we should now close the borders.
“I don’t think it would be wise nor would it make sense.”
He said: “While the thought that a terrorist could use the guise of a refugee is a horrific one, the vast majority of refugees are the victims of evil.
“They are not the perpetrators of evil and I was able to speak to so many of them and hear how they and members of their families have suffered so tremendously at the hands of the perpetrators of evil.”
He said countries with large numbers of refugees passing through their borders needed to do more to ensure security checks were being carried out.
“There is no doubt that in Turkey and Greece the authorities need to step up their operations and need to be far more vigilant with people passing though their territories.”
He added: “My visit to the camp has reinforced for me how important it is that we are helping, and how much more we have to do - particularly as the winter months are about to set in and in the next few months they will be facing additional danger.”