"Well, look, it was Mayor de Blasio's skit. He has addressed it, and I will really defer to him because it is something that he's already talked about," Clinton told Cosmopolitan in an interview published Tuesday when asked if she thought the joke was "inappropriate."

De Blasio told CNN on Monday that the skit was "clearly staged."

"It was a scripted show. The whole idea was to do the counterintuitive by saying 'cautious politician time.' Every actor thought it was a joke on a different convention. That was the whole idea. I think people are missing the point here," he said.

His office also released a statement later saying that the skit was only meant to poke fun at the mayor himself, according to NBC News

"In an evening of satire, the only person this was meant to mock was the mayor himself, period. Certainly no one intended to offend anyone," the statement said.

President Obama's top spokesman Josh Earnest on Tuesday defended de Blasio and Clinton, saying the two have "demonstrated a genuine commitment to the pursuit of equality and justice and civil rights." But he said he had not himself heard the joke.

“I can’t speak to any misguided attempts at humor,” he said. “I can only speak to their commitment they have shown over the course of their career to justice and civil rights."