The interview began with Mr. Hannity playing a clip of Mr. Bloomberg talking about his stop-and-frisk policy of throwing young men against walls.

“Thank you for playing that for your millions of viewers, because now more people are going to see who Mike Bloomberg really is,” Mr. de Blasio said.

The mayor’s attacks have angered Mr. Bloomberg’s allies, who have mostly avoided criticizing Mr. de Blasio even during his fleeting run for president last year. That informal policy has clearly ended.

“Few public officials anywhere are as innovative and clever as Bill de Blasio when it comes to repeated efforts at money laundering,” Stu Loeser, a spokesman for Mr. Bloomberg, posted on Twitter, referring to Mr. de Blasio’s questionable fund-raising practices.

Mr. Loeser said it was his decision, not Mr. Bloomberg’s, to speak out against Mr. de Blasio.

“If he wants to present himself as an opinion maker to the American people, we’re going to have to remind people about his full legacy in office,” Mr. Loeser said in a phone interview, pointing to a de Blasio donor who pleaded guilty to using campaign contributions as bribes.

Mr. de Blasio’s attacks are a desperate attempt to gain relevance, Mr. Loeser said.

“It’s no secret that Bill de Blasio loves national politics and loves it more than being mayor,” he said.