The Miami school superintendent who accepted, then rejected a job as New York’s schools chancellor Thursday says he backed out at the last minute because Mayor Bill de Blasio wouldn’t let him pick his own staff — and then jumped the gun on leaking the news, according to a new report.

Educator Alberto Carvalho has publicly claimed the change of heart came because parents and students begged him to stay on in Miami during a lengthy televised school board meeting.

But he’s been telling other people that he actually started having second thoughts after accepting the gig a week ago because de Blasio pulled a “power play” on him, according to a Politico report.

For one, he says, Hizzoner wasn’t going to let the new schools boss pick his own chief of staff or head of human resources, and planned to keep outgoing Chancellor Carmen Fariña in a vague role for an indeterminate period of time, the site reports.

But the straw that broke the camel’s back was apparently when de Blasio went public with the news that Carvalho had taken the job Wednesday night — before the Floridian was ready to make the announcement, he says.

De Blasio’s spokesman denied all of those claims Friday.

“It’s literally and entirely wrong,” Eric Phillips told The Post.

City Hall officials claim that, in fact, the news came out early because Carvalho kept telling people he was leaving and word spread, and pointed out that Fariña has already said she’s leaving at the end of the month.

De Blasio himself claimed Thursday that Carvalho had given his thumbs up about letting the press know about the appointment.

“He said yes over a week ago, he authorized the story being given to Politico,” de Blasio told reporters.