"Since he apologised and retracted his remarks, as far as (I) am concerned, the matter is over," Intelligence and Transport Minister Israel Katz said in a statement, citing the "tremendous importance of historical truth and remembrance" of the victims of the Holocaust.
Trump spokesperson sparks outcry by comparing Assad to Hitler
Spicer made the assertion at a daily news briefing, during a discussion about the April 4 chemical weapons attack in Syria that killed 87 people. Washington has blamed the attack on the government of Syrian President Bashar al Assad.
"You had someone as despicable as Hitler who didn't even sink to using chemical weapons," Spicer said when asked about Russia's alliance with the Syrian government.
The Nazis murdered six million Jews during World War Two. Many Jews, as well as, others were killed in gas chambers in European concentration camps.
When a reporter asked Spicer if he wanted to clarify his comments, he said: "I think when you come to sarin gas, there was no, he was not using the gas on his own people the same way that Assad is doing."
Later on Tuesday, Spicer apologised and said he should not have made that comparison.
"It was a mistake. I shouldn't have done it and I won't do it again," Spicer told CNN in an interview. "It was inappropriate and insensitive."
Spicer's assertion, made during the Jewish holiday of Passover, sparked instant outrage on social media and from some Holocaust memorial groups who accused him of minimising Hitler's crimes.
Katz, a member of Prime Minister Benjamin Netanyahu's party, had tweeted late on Tuesday that Spicer's comments at the news briefing were "grave and outrageous", and he said the White House spokesperson should apologise or resign.
White House accuses Russia of Syria chemical attack 'cover up'
There was no immediate comment from other Israeli leaders, during a Passover holiday period when government business is largely at a standstill and many in the country are on vacation.
It was not the first time the White House has had to answer questions about the Holocaust. Critics in January noted the administration's statement marking International Holocaust Remembrance Day, which omitted any mention of Jewish victims.
At the time, Spicer defended that statement by saying it had been written in part by a Jewish staff member whose family members had survived the Holocaust.
Despite these difficulties, relations between Trump administration and the Israeli government have been more cordial than under the Obama presidency, although differences remain over the scope of Israeli settlement-building.
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