The film producer Harvey Weinstein and the veteran Broadway press agent Rick Miramontez have parted ways on Mr. Weinstein’s forthcoming musical “Finding Neverland” after sharp words were said at their weekly planning meeting on Tuesday — a rare rupture in the image-conscious world of Broadway and another bump in the road for a highly anticipated musical.

With the big-budget “Finding Neverland” set to begin performances in March, Mr. Weinstein — who is making his debut as a Broadway lead producer — said on Thursday night that he raised a series of concerns about media coverage during the

meeting with the musical’s press agents and advertising team. Chief among them was the lack of feature stories in the works by prominent magazines about the musical and its stars, Matthew Morrison and Kelsey Grammer — the sort of coverage that can help generate ticket sales on Broadway, where 75 percent of shows close at a financial loss.

“We had no long lead stories lined up for GQ, Vanity Fair, New York magazine, and I went around the room with Rick and his team and asked, ‘Who is the editor of GQ?’ and other rudimentary questions that they had no answers to,” Mr. Weinstein said, making a reference to lengthy magazine and newspaper stories that are planned long in advance of publication. “Our only long lead story planned was in Vogue, and I arranged that. We used to kid Rick and O&M that Broadway.com is great but we have to think outside the box for musicals,” referring to a theater website that is read more by Broadway insiders than the general public.

“Rick is the finest on Broadway,” Mr. Weinstein added. “We had our creative differences. I’m sure Rick has his own side of the story and he is one of the wittiest people I know, even though those quips will be at our expense. And I’m sure that we will ask him to come back at Tony Awards time.”

Mr. Weinstein made the comments on Thursday night after being informed that Mr. Miramontez had confirmed that he had resigned on Wednesday from the musical.

Mr. Miramontez said by email on Thursday night: “If I were a headline writer I’d go with this: BROADWAY TO HARVEY WEINSTEIN: DROP DEAD.”

“Our track record speaks for itself,” Mr. Miramontez said in another email. “It would come as no surprise to anyone who has ever worked for him that Harvey’s hunger for publicity doesn’t always align with the realities of the real world. That said, we still love ‘Finding Neverland.’ ”

Mr. Miramontez also disputed Mr. Weinstein’s characterization of the part of the meeting dealing with magazine stories on “Finding Neverland.”

“We did discuss GQ, but his bizarre pop quiz on their editorial staff, which we ended up passing with flying colors, was not the problem,” he said. “The problem came when he demanded that they give Finding Neverland a cover. He doesn’t understand that the nation’s top men’s magazine is not going to devote a cover to his Broadway show. The reality is, at this point, they don’t even want to devote a page to it. He’s just having a tough time facing facts.”

After making his comments, Mr. Weinstein sent an email at 12:58 a.m. Friday trying to put a positive spin on things.

“If I knew a little more about Broadway none of this would have happened – ultimately, I have to take responsibility of this,” he said. “This is my fault for my inexperience. Rick is working for my company on the movie ‘The Last 5 Years’ and doing a bang-up job – but I’m hovering over ‘Finding Neverland’ too much and I have to let go a little bit. I’ll be begging Rick to come back by tomorrow.”

Mr. Miramontez declined to discuss the specific reasons he resigned the “Finding Neverland” account. But two people who were at Tuesday’s meeting said that Mr. Miramontez had been annoyed that Mr. Weinstein arrived late — accounts vary on how late, with Mr. Weinstein saying it was a matter of minutes — and then troubled when Mr. Weinstein chided various people there, including members of Mr. Miramontez’s team from his company, O&M.

The two people, who spoke on the condition of anonymity to describe a confidential meeting, said that Mr. Weinstein was critical of the digital publicity and marketing plans for the musical. (Mr. Weinstein, in the interview, said he had used digital tools successfully on his recent movie “Paddington,” among other films.) The two people said that Mr. Weinstein used profanity at times; Mr. Weinstein adamantly denied doing so.

“No profanity, but I was tough. I said, ‘we will need to fire you, you will need to tender your resignation or you will need to show us a plan to have strong print coverage and digital strategies,’ ” Mr. Weinstein said.

On one level, the falling-out reflects a clash of cultures. Mr. Weinstein, while a longtime investor in Broadway shows, is a hard-charging, hands-on producer who is used to doing business directly with top magazine editors, with whom he has deep connections, and often getting his way. Many Broadway producers, by contrast, tend to collaborate closely and respectfully, and sometimes deferentially, with their press agents, especially a well-respected veteran like Mr. Miramontez, whose shows are often nominated for and regularly win Tony Awards. Resignations like Mr. Miramontez’s are rare in the discreet world of Broadway: The last major one was in 2010 when Boneau/Bryan-Brown quit the troubled musical “Spider-Man: Turn Off the Dark” and was replaced by Mr. Miramontez.

Indeed, Mr. Weinstein was amused that the departure of a Broadway publicist would be newsworthy.

“If I knew The New York Times would cover a publicist leaving a production, I would arrange to hire a publicist one day, fire him the next day, and then rehire the publicist the following day just for the publicity,” he said.

He also tipped his cap to one of his chief rivals in the film world, Scott Rudin, who is a highly successful Broadway producer with a blockbuster musical, “The Book of Mormon,” and a string of critically acclaimed and commercially popular plays in recent years.

“One reason Scott Rudin is the best producer on Broadway is because he thinks outside the box and he works hard to get extensive coverage for his shows in all the major magazines and newspapers,” Mr. Weinstein said.

“Finding Neverland,” based on the 2004 movie about J.M. Barrie and the creation of Peter Pan, has had a bumpy road to Broadway but is nevertheless awaited with much anticipation, given Mr. Weinstein’s talents as a producer and the musical team he has assembled.

An earlier version of the musical opened in 2012 in Leicester, England, with Mr. Weinstein hoping to bring it to London and New York. Instead, after feedback from friends like Bono and Andrew Lloyd Webber, he junked the entire show – at a cost of several million dollars – and fired the creative team. To build a new “Neverland,” he hired the Tony-winning director Diane Paulus (“Pippin”); the songwriters Gary Barlow and Eliot Kennedy; and the playwright James Graham. It had a run last summer at Ms. Paulus’s theater, the American Repertory Theater in Cambridge, Mass., where it broke box office records and received both positive and mixed reviews.

Mr. Weinstein subsequently replaced the star of the Cambridge production, the Tony nominee Jeremy Jordan, with Mr. Morrison, a theater veteran and television actor best known for “Glee.” Another key actor in Cambridge, the Tony winner Michael McGrath, is also not coming to Broadway with the show, replaced by Mr. Grammer, an Emmy Award winner for “Frasier.”

Mr. Weinstein, asked who the new publicist would be for “Finding Neverland,” said he may end up handling it in-house.