BOSTON — Local universities expressed concern Tuesday that a proposed College Athletes Bill of Rights would cost them scholarships and commit them to lifelong health insurance for players who are injured during games.

Testifying at a Boston City Council committee hearing, representatives from the area’s Division I schools balked at provisions that they said would put them at a competitive disadvantage on the field and burden already money-losing athletic department budgets.

The College Athletes Bill of Rights proposed by City Councilor Josh Zakim would require schools in the city to offer four-year scholarships, instead of the renewable one-year grants the NCAA currently allows. It would also require schools to cover athletes’ medical expenses for any sport-related injuries – for the rest of the player’s life.

“I think this is an area the city has an opportunity to lead on,” Zakim said.

Zakim also introduced a separate bill that would create a head-injury protocol that would apply to any games played in Boston.

The school representatives said they were in favor of protecting students but questioned whether the city should be the one to regulate them. On Monday, the NCAA issued guidelines that recommended a limit of two contact practices per week, but Zakim said it didn’t go far enough.

“They (the NCAA) are a non-governmental body; these guidelines are non-binding,” he said. “Why shouldn’t the city take the lead?”

The ordinance was filed in May, and Tuesday was an opportunity for the public to comment. Daniel Sibor, Zakim’s chief of staff, said the proposal now goes to working sessions to hammer out the language with the hope of a vote in the fall.

Among those testifying before the city’s Committee on Government Operations on Tuesday were representatives from Boston College, Boston University, Northeastern and the Association of Independent Colleges and Universities. Also speaking were Chris Nowinski, of the Sports Legacy Institute, which has led the national debate on head injuries in sports, and Ramogi Huma, the head of the National College Players Association.

“We’re being stonewalled by the NCAA, the conference commissioners and all the schools,” Huma said. “I think we can get a standard in (this) way.”

Under the bill of rights, schools in the city would be required to offer injured or cut athletes equivalent, nonathletic scholarships for a total of five years or until the athlete graduates, whichever is sooner. (Scholarships could be withdrawn for disciplinary or academic reasons.)

Other provisions would require the school to provide athletes with “financial and life skills” and promise the athlete the same disciplinary rights as other students.

Calling for a “Right to Health and Safety,” the ordinance also would require schools to provide athletes with comprehensive, year-round medical care, and to train athletes and staff in concussion and dehydration awareness. The head-injury ordinance also filed by Zakim creates a protocol that would prevent players from returning to games after a concussion or becoming unconscious.