Tony Abbott's comments were made amid calls by a former commander of coalition forces in the Middle East for Australia to join US-led airstrikes in Syria.
Tony Abbott made the contentious remarks on Sydney commercial radio 2GB.
"I mean, the Nazis did terrible evil but they had sufficient sense of shame to try to hide it. These people boast about their evil."
He was asked later whether he stands by his comments that suggest IS militants are worse than the Nazis.
"Well I think you're trying to put words in my mouth I stand by what I said and not by the interpretation that other people might want to put on it."
The Opposition leader, Bill Shorten, says it's not a comparison he'd draw.
"Well listen there's no doubt that IS is evil and bad and terrible but I'm not sure I'd compare it to the whole Second World War."
Executive Council of Australian Jewry president Robert Goot describes Mr Abbott's comparison as "injudicious and unfortunate".
He says the crimes of self proclaimed Islamic State are indeed horrific, but cannot be compared to the systematic round-up of millions of people and their despatch to purpose-built death camps.
At least ten people have been killed and dozens wounded when a car bomb exploded in the Syrian city of Latakia, a rare attack in a coastal city mostly loyal to President Bashar al-Assad.
General David Petraeus is a former commander of coalition forces in the Middle East.
He say one way to destroy IS is to attract and co-opt moderate members of Al Qaeda's affliliate group in Syria.
"It should not be cooperating with the leaders of an Al Qaeda affiliate, Jabhat Al Nusra. It should certainly consider doing what we did in Iraq, where we were confronted by an industrial-strength extremist insurgent movement, Al Qaeda in Iraq and associated Sunni Arabic insurgents."
In an address to the Lowy Institute in Sydney he says terrorism today poses an unprecented threat.
"The result is we see the creation of multiple terrorist sanctuaries on a scale unparalleled since 9/11. Only now they are just a stone's throw from Europe."
The retired four-star US general served as commander of Coalition forces in Iraq and Afghanistan.
He says airstrikes in Syria are an important part of the fight against Islamic State.
"I think that taking such an action, together with the other coalition members, will do damage to ISIS, it'll add, complement, augment the actions of the US and the other coalition partners that are indeed engaged in ISIS not just in Iraq but in Syria as well."
He's encouraging Australia to agree to the recent US request for help.
"But at the end of the day there's a reason why the coalition countries and the US have taken that action and again, I think that that is one that ultimately would be one that Australia should consider with that in mind."
Prime Minister Tony Abbott says a decision will be made when the Defence Minister returns from overseas next week.
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