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Hillary Clinton’s response to a racially charged comedy sketch with Mayor Bill de Blasio of New York on Saturday night was simple: It’s all his fault.

“Well, look, it was Mayor de Blasio’s skit,” Mrs. Clinton told Cosmopolitan magazine. “He has addressed it, and I will really defer to him because it is something that he’s already talked about.”

Mr. de Blasio’s office said he was poking fun only at himself at the satirical Inner Circle dinner in Manhattan, when he joked with Mrs. Clinton at the annual black-tie event that he had been late to endorse her candidacy because he was “running on C.P. time.” a reference to the stereotypical “Colored People Time.” The line drew some cringes from the audience.

Mrs. Clinton jumped in at the prearranged skit: “Cautious politician time,” she said. “I’ve been there.”

The exchange prompted a mix of ridicule and bafflement on social media. Mr. de Blasio told CNN on Monday night, “It was clearly a staged show, a scripted show and the whole idea was to do the counterintuitive and say cautious politician time.”

He said Mrs. Clinton, who is trying to court black voters ahead of the April 19 New York primary, and the other participant in the skit, Leslie Odom Jr., the actor who plays Aaron Burr in the hit musical “Hamilton,” were both in on the joke. He said that they both “thought it was a joke on a different convention” and that “people are missing the point here.”

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