To Eileen Boyle, the mayor is opening a can of worms.

The Savin Hill activist with “Save Our City,” a group that wants all municipal workers to be required to live within city limits, took exception on Monday night to Martin J. Walsh’s proposal to lift the residency rule for certain high-level city positions.

On May 30, Walsh filed the proposal with the City Council, although the move did not become public until late Monday afternoon. That evening, at the monthly meeting of the Columbia Savin Hill Civic Association, which Boyle chairs, she said, “This is not good news. It’s not good news for the city.”

In a statement issued from City Hall on Tuesday morning, the mayor’s spokesperson, Kate Norton, said “Mayor Walsh’s proposal to explore a waiver for residency in exceptional cases is about expanding and broadening our recruitment options. He seeks to hire the most qualified candidates to serve the city of Boston.” If approved, the proposal would allow Walsh to waive the residency requirement for any person or position by filing a letter with the city clerk with the individual’s name, address, and appointed position.

Boyle’s issues with the request were specific: It appears geared toward high-profile, high-paying positions, and “sets a bad precedent.” Boyle lamented the notion of the mayor telling his lower-paid city workers that you have to stay in the city but he is going to appoint the person that’s “making $150K” who can stay outside the city. “I believe that we have plenty of talent that is in the city,” she said. “Mayor Menino seemed to be able to find those people.”

Annissa Essaibi George, a former candidate for City Council who once led the Columbia-Savin Hill Civic Association, was surprised by Walsh’s move.

“I think that we have a lot of talent here in Boston and we need to embrace and support that especially when it comes to high ranking officials,” she said, adding that she hopes the City Council rejects the proposal.

“Mayor Walsh is doing a fantastic job,” said Essaibi George. “I’m proud to have him as my mayor, but I do think that this is one of those issues that I hope that he reconsiders.”

Boyle has been working to bring the issue to Walsh’s attention since he arrived at City Hall in January. She wants Walsh to strengthen the requirements, which were weakened during Menino’s tenure. Under current requirements, any person may apply for a job in the city of Boston, but the selected applicant must be a Boston resident on his or her first day of work and remain a Boston resident while working for the city.

There are, however, exceptions to the policy. Certain union members, such as law enforcement and firefighters, may be exempt from the residency requirement in line with a relevant collective bargaining agreement. And under state law, Boston’s public school teachers are not required to live in the city.

In a letter addressed to Walsh and dated April 9, Boyle laid out five recommendations for strengthening the residency requirement. They included mandating that anyone taking police or fire exams prove residency two years in advance and not allowing promotions for any city employee who moved outside of the city.

“Watching cities across the country one thing remains clear, cities that have a residency ordinance are economical [sic] doing much better than those that are not,” Boyle wrote in the letter, which she delivered to the mayor’s chief of staff, Daniel Koh.

Walsh has yet to fill a number of key positions: chief of arts and culture, streets, transportation, and sanitation. In one early instance, Walsh said in January that Joe Rull, a non-resident whom he appointed to his cabinet as director of operations, would move into the city as required.

In 2006, the city council held two hearings on the residency requirement. Councillor John Tobin of West Roxbury sought to push through an ordinance that would require all city employees to stay for only five years, but backed off when it appeared he didn’t have the votes to get it passed.

Councillor Matt O’Malley, who represents Jamaica Plain and West Roxbury, was the only councillor to weigh in on the matter at Wednesday’s City Council meeting. He expressed “grave concerns” about the mayor’s proposal, which he said would “exacerbate” unfairness among city workers. The proposal now moves to the Committee on Government Operations.