"It's unfortunate and we should never have comparisons with Hitler ever," Haley told CNN. "That was a terrible time in history and it's just not something people want to hear about or think about or think there's another comparison to it."
Spicer made the comparison as he tried to condemn Russia's alliance with Assad in the wake of the horrific chemical attack in Syria last week.
"You had a — you know, someone as despicable as Hitler, who didn't even sink to using chemical weapons," Spicer said.
Asked by ABC News' Cecilia Vega to clarify his comments, he gave a further muddled response, saying of Hitler, "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."
"But I'm saying that in the way that Assad used them, where he went in towns, dropped them down to innocent — into the middle of towns — it was brought, so the use of it — I appreciate the clarification," he said, concluding, "That was not the intent."
After the briefing, Spicer offered another clarification on his comments.
"In no way was I trying to lessen the horrendous nature of the Holocaust," he said in a statement. "I was trying to draw a distinction of the tactic of using airplanes to drop chemical weapons on population centers. Any attack on innocent people is reprehensible and inexcusable."
Despite the explanation, Spicer's words drew widespread condemnation, including a call for his firing from House Minority Leader Nancy Pelosi of California.
"While Jewish families across America celebrate Passover, the chief spokesman of this White House is downplaying the horror of the Holocaust," she said in a statement. "Sean Spicer must be fired, and the president must immediately disavow his spokesman's statements.
"Either he is speaking for the president or the president should have known better than to hire him," Pelosi added.
Democratic National Committee Chairman Tom Perez called on Spicer to apologize for his comments.
And the Anne Frank Center condemned Spicer's statements.
ABC News' Katherine Faulders contributed to this report.