Jewish leaders say Tony Abbott’s comment suggesting Islamic State terrorists are worse than the Nazis is “injudicious and unfortunate”.

The Prime Minister told radio 2GB on Thursday the extremist group, which Australia is fighting in Iraq, was responsible for many atrocities.

“The Nazis did terrible evil but they had a sufficient sense of shame to try to hide it,” Mr Abbott said.

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“These people boast about their evil, this is the extraordinary thing.

“They act in the way that medieval barbarians acted, only they broadcast it to the world with an effrontery which is hard to credit.”

Executive Council of Australian Jewry president Robert Goot said there was a “fundamental difference between organised acts of terrorism and a genocide systematically implemented by a state as essential policy”.

“Whilst there is no question that Islamic State is a profoundly evil organisation, the prime minister’s comments suggesting that it is in some respects worse than the Nazis were injudicious and unfortunate,” Mr Goot said.

“The crimes of Islamic State are indeed horrific, but cannot be compared to the systematic round-up of millions of people and their dispatch to purpose-built death camps for mass murder.”

Those responsible for state-sponsored genocide were high government officials who operated in secret “not out of any sense of shame, but to avoid being held criminally responsible for their actions”, he said.

Mr Abbott later said he wasn’t in the business of ranking evil but stood by his comments.

“I do make this point, that unlike previous evil-doers, whether we’re talking about Stalin, Hitler or whoever, that tried to cover up their evil, this wretched death cult boasts about it,” he told reporters in Melbourne.

The government is next week expected to announce how it will respond to a United States request for Australian military operations in Syria.

Opposition Leader Bill Shorten said Islamic State was “evil” and should be fought.

“But I don’t think I would equate it with World War II,” he said.