Already hobbled by the retirements of a dozen colleagues, the state premier on Thursday disclosed his controversial costume choice amid rumours about the 2003 party.
"Dominic Perrottet has my support and he also has the support of the Nationals," Deputy Premier Paul Toole told 2GB on Friday.
"He admitted he's done something stupid but we've all done something stupid (and) insensitive and there are things that we all probably regret when we were 21."
Treasurer Matt Kean - a potential leadership rival - had earlier also thrown his support behind the premier.
But former Labor premier Bob Carr said the 40-year-old Perrottet was now unelectable.
"Will Jewish leadership insist on his resignation? They should. The memory of six million demands it. He must go," he said.
"If some kid in western Sydney who didn't know better, scrawled graffiti on a synagogue, they would be demanding prosecution under the new provisions of the crimes act."
Mr Perrottet's confession was prompted by a cabinet colleague's private warning on Tuesday.
Seven News named Transport Minister David Elliott as that colleague.
"At that age in my life, I just did not understand the gravity of what that uniform meant," Mr Perrottet said on Thursday.
"It was just a naive thing to do ... I'm truly sorry for the hurt and the pain this will cause right across our state."
Asked where he saw the humour in wearing a Nazi uniform, he suggested all people matured differently based on their experiences.
"I am not the person I was when I was 21," the 40-year-old said.
"At that time, the pages of the history books had not had the impression on me that they should have."
The incident came a year after Mr Perrottet joined the NSW Liberal Party and two years before he was appointed president of the NSW Young Liberals.
In the two decades since Mr Perrottet hired the Nazi costume and walked into his birthday party, attitudes have evolved, renowned Australian Jewish historian Suzanne Rutland said.
"There's been a much greater sensitivity that is developed over the years to these types of issues," she told AAP.
Dr Rutland noted it was only last year that the swastika was banned in NSW and Victoria.
"And yet there have been problems with the swastika for years - it didn't get banned at that point in time," she said.
Cultural historian Jordana Silverstein said the timing of the premier's admission was about saving face, rather than genuinely accounting for his actions.
"It's always been considered offensive, but it's a matter of whose opinions have been listened to, and respected," she told AAP.
"(Mr) Perrottet wearing the Nazi costume speaks to the normalisation of anti-Semitism and how acceptable it is amongst a certain segment of Australian society."
The NSW Jewish Board of Deputies accepted a personal apology from the remorseful premier and said it hoped "this unfortunate incident will serve as a lesson to all".
Followers of the Board of Deputies were divided about the significance of the incident, which the premier has cast as a terrible mistake of youthful naivety.
While some said the public knew well in 2003 that dressing as a Nazi was offensive, others said young men like Mr Perrottet didn't have the inherited experience and education about the Holocaust.
Polls for the state election open on March 18.
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