“You must understand the anger and frustration of those who feel strongly that taxpayer dollars and corporate funds should not be devoted to supporting this event,” Mr. Kenney wrote in the letter, dated Jan. 21.

The Mummers divisions loosely organize many groups under broad banners — there is a Comic Division and a Fancy Brigade — and their leaders have always struggled to police the behavior of groups and participants. Mr. Kenney, himself a former Mummer, requested a meeting of the leaders with the city’s managing director, and proposed several changes to how the Mummers organize.

“We agree with his chain of thought that some things have to be improved,” said Richard Porco, the president of the Comic Division. He said that the groups had improved “a lot over the past four or five years,” pointing to sensitivity training in 2016 and increased city oversight of the themes chosen by the groups.

Mr. Porco said that the two marchers with black-painted faces this year had put on makeup during the course of the parade, calling them “two knuckleheads that took it upon themselves to put blackface on out of 10,000 marchers, approximately.” He said that the Mummers do not condone blackface, but found it difficult to police amid the thousands of people wearing colorful costumes and makeup.

“We try to stop it,” he said. “But it’s going to be a hard road to haul.”

On Thursday, Councilwoman Cindy Bass introduced a bill that would penalize people who wear blackface at the parade, including with a $75 fine and a ban of up to five years from the parade. The bill is not final, she said in an interview on Friday, noting that it would have to take into account legal protections for free speech.