The mother tiger, named Hana, had given birth to three cubs after being mated with a tiger from Germany called Avigdor, Nili Avni-Magen told AFP.
"One cub died shortly after birth but the other two were in good health. We discovered they had been killed when we went to weigh them," she said.
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"We have no explanation for the behaviour of the mother, who had taken good care of them at the start."
Listed as critically endangered by the International Union for Conservation of Nature, just 400 Sumatran tigers survive in the wild on the Indonesian island.
But captive breeding programmes have raised their number in zoos around the world to 261 from 180 in 2008. This year, 32 were born in captivity.
The Jerusalem Biblical Zoo, which boasts a collection of wildlife mentioned in the Hebrew Bible, is also known for its success in breeding endangered species.