Adult-film star Stormy Daniels speaks to the media in April along with lawyer Michael Avenatti, on right, outside federal court in Manhattan. (Brendan Mcdermid/Reuters)

Prosecutors investigating Donald Trump’s former attorney, Michael Cohen, scuttled a Monday interview with adult-film star Stormy Daniels after word of it leaked to the press, setting off a heated exchange about the cancellation with her lawyer.

The interview by prosecutors in the Southern ­District of New York was scheduled in advance of a potential grand jury ap­pearance about a $130,000 payment from Cohen in exchange for her silence about an alleged affair with Trump, according to a person familiar with the investigation. 

After the planned interview was reported in The Washington Post on Sunday, Michael Avenatti, Daniels’s attorney, announced on Twitter that prosecutors had canceled “because the press found out about the (meeting) and they can’t handle a few cameras outside their offices. If they consider this a big deal, how will they ever bring any serious criminal charges against Cohen et al., let alone handle a trial, in such a high profile matter?”

He added, “They don’t appear to have the stomach for a case of this magnitude unfortunately.”

A spokesman for the U.S. attorney’s office declined to comment Monday morning. Late Sunday, Assistant U.S. Attorney Nick Roos accused Avenatti of leaking the report of the meeting.

“Such leaks are inappropriate in and of themselves, and more importantly, call into question your commitment to maintaining the required confidentiality of the substance of our meeting with your client,” Roos said in an email provided to The Post by Avenatti. “For these reasons we have cancelled our meeting, and will reassess how to proceed.” 

Avenatti also provided to The Post his emailed responses, in which he offered to change the location of the meeting and called the cancellation “a disgrace and completely unprofessional.”

The tense back-and-forth comes less than one month after Avenatti, who has attacked the president and Cohen in frequent television interviews, was rebuked by a New York judge for conducting a “publicity tour.” That led Avenatti to withdraw his request to get involved in a court dispute over records seized in the federal raid in April of Cohen’s home and office. Cohen is under federal investigation for possible campaign finance violations as well as bank and wire fraud.

His attorney, Stephen Ryan, declined to comment Monday.

A June 1 email exchange with Roos also provided by Avenatti offered a glimpse into the discussions about Daniels’s potential testimony before a grand jury.

Roos wrote: “To confirm our conversation, we are excusing Ms. Clifford’s appearance before the grand jury on June 15 on the understanding that she will appear voluntarily for an interview in the month of June. Please let us know once you have possible dates for an interview.”

Cohen has acknowledged making the payment to Daniels, whose real name is Stephanie Clifford, through one of his Delaware business entities. The payment came in the final weeks of Trump’s presidential campaign, and Trump has recently said he was aware that Cohen made an arrangement with Daniels.

White House officials have repeatedly denied that Trump had a sexual relationship with Daniels.

Daniels is suing Trump and Cohen in California to invalidate the confidentiality agreement she signed at the time of the payment. A federal judge in April granted Cohen’s request for a delay, saying it appeared likely that Cohen would be indicted in the criminal investigation in New York.

She is also suing the president for defamation in New York federal court; a response to her claim is due by July 23. 

Cohen is also under scrutiny by special counsel Robert S. Mueller III in the investigation into Russian interference in the 2016 election.

Devlin Barrett contributed to this report.