After several days of vocal pushback to outdoor dining fees in the North End, Boston Mayor Michelle Wu on Tuesday sought to tamp down the simmering dispute with restaurant owners by restructuring the special requirements in the neighborhood for participation in the city’s temporary outdoor dining program.

“I believe we can come to a situation this summer where our community members — which includes our residents and our restaurant owners — are all thriving,” Wu said at a press conference.

Restaurateurs in that neighborhood have bristled at being forced to pay a $7,500 participation fee, as well as a monthly parking fee, to participate in the outdoor dining program. That program launched in 2020 to help restaurants survive the COVID-19 pandemic, and it will remain free for establishments in other neighborhoods. North End restaurant owners have also voiced displeasure at being given a shorter window in which outdoor dining can occur. The program will run there from May 1 through Sept. 30, compared to April 1 through at least Dec. 1 in other sections of the city.

On Tuesday, though, Wu announced that some North End restaurants will now be allowed to pay a reduced annual fee of $5,000 or $3,500, depending on location and outdoor footprint and whether they own a liquor license. Establishments in the neighborhood will also have the options to pay the fee in increments or pay a smaller amount to serve outdoors for a shorter period of time.

“This is something that we want to work all across the city,” Wu said. “It has to be specifically tailored for the impacts that it has in different parts of the city as well.”

In a letter sent to North End restaurants last Friday, Wu said establishments there are being treated differently because they have an unusually high impact on the surrounding community. Last summer, Wu wrote, the North End had more than three times as many restaurant patios as any other neighborhood. She said that resulted in a dearth of parking spaces, problems with rodents and cleanliness, and intense frustration from North End residents.

Wu also noted in the letter that the entire outdoor dining program will be reassessed after it concludes this year. The mayor closed with what was widely read as a warning. “If a critical mass of restaurant owners also believe this program is unworkable as proposed,” Wu wrote, “then I am prepared to rescind North End outdoor dining before the start of this season.”

On Tuesday, Wu insisted that the line in question had been misread.

“You would know if I was threatening something,” she said. “It wasn’t a threat. I was clarifying.”

The mayor was flanked by Boston City Councilor and state Sen. Lydia Edwards, who represents the North End; House Ways and Means Chair Aaron Michelwitz, who represents the neighborhood and lives there; and restaurateurs Nick Varano and Philip Frattarolli. All of the other speakers lauded Wu for striking a suitable balance between the needs of local residents and businesses.

“I believe if we can come together and figure this out this year, we can have this for a longer time,” Varano said. “We can have this for the years to come. But if we don’t, it’s going to be something that’s lost.”

Wu, who used to live in the North End, earned more votes in the neighborhood during last year’s mayoral election than competitor Annissa Essaibi George, but her margins there were narrower than in other parts of the city.