BOSTON >> The owners of five restaurants in Boston’s North End say in a lawsuit against Mayor Michelle Wu that the city’s $7,500 fee for eateries in the neighborhood that want to offer outdoor dining this summer is unconstitutional.

The four business owners, in their federal complaint filed Monday, said the fee — which applies only to restaurants in the traditionally Italian neighborhood that attracts tourists from around the world — creates “unfair methods of competition.”

The fee violates the restaurant owners’ constitutional due process and equal protection rights, and their rights under the commerce clause, the restaurateurs assert.

The mayor’s office said in a statement it had no comment. Wu has said that because the North End — with its maze of narrow and busy streets — has the highest density of restaurants in the city, the fees are necessary to address quality-of-life issues like traffic, pedestrian access, trash collection and rodent control.

All four owners said they agreed to pay the fee under protest. One owns two establishments.

“If plaintiffs refused to pay the fees … they would not be allowed to have outdoor dining spaces,” the lawsuit read. “Without outdoor dining, plaintiffs would not be able to compete with other North End restaurants” catering to tourists.

The city first allowed restaurants to set up al fresco dining areas on sidewalks and city streets two summers ago to help them stay in business during the COVID-19 pandemic. Outdoor dining in the neighborhood resumed May 1.

The city announced the fee in March, but business owners pushed back, calling it unfair because it did not apply to restaurants in other areas of the city.

The city and some restaurant owners announced a compromise in late March that allowed businesses to spread the fee out over several months, and a plan that allows some restaurants to pay reduced fees based on location, the size of their outdoor dining area, and whether they have a liquor license.