The Boston city council is choosing to further study a “just cause” eviction ordinance proposed by Mayor Martin Walsh in order to incorporate feedback from an extended meeting and community input.

The “Jim Brooks Stabilization Act,” named after the late longtime Roxbury activist, would need to be passed by the city council and the state legislature to take effect. It is designed to “protect residential tenants and former homeowners living in their homes post-foreclosure against arbitrary, unreasonable, discriminatory, or retaliatory evictions, and help ensure that tenants and former homeowners are aware of their rights under state law,” according to a release from the mayor’s office.

The Jim Brooks act would codify conditions under which landlords could evict tenants, including but not limited to: failure to pay rent, violating the lease terms creating a nuisance or damaging the property, or using the unit for illegal purposes. Landlords that want to take possession of a unit for his or her own use or that of immediate family members would also be able to evict tenants.

Landlords would also have to notify the City of Boston’s Office of Housing Stability about intent to evict within two days of serving notice. The office would then notify tenants and former homeowners of their rights via mail.

Those concerned about the measure worry about the impact on landlords controlling seven units or more, who would be subject to new rules for evictions. The Cambridge-based Small Property Owners Association has said in mailing that the bill would devalue affected rental housing and raise the tax burden on most residents.

At the beginning of a six-hour hearing on Monday, Sheila Dillon, the city’s housing chief, said housing pressures are having a dire impact on the affordability of the city.

“As all of you know, the city of Boston has very, very high housing costs right now,” she said. “And some reports have us as the third highest in the country. And we’ve become and unaffordable city because our population is growing, in leaps and bounds.”

Demographers estimate that the city could add 50,000 new residents in the next 20 years.

“And that population growth is putting a lot of pressure on our existing rental stock,” Dillon said. “And our housing has not kept pace with these trends. The result has been that people are competing for too few available units.”

Around 37,000 low-income households are paying over half of their income in rent, she said, as are more than 5,000 elderly households.

“I agree in theory with this,” said City Council President Michelle Wu at the hearing. It helps tenants in two ways, in evening the dynamics of power between tenant and landlords, she said.

“One is around notification requirements, which will enable the city to have a better idea and potentially deploy resources to help people know their rights,” she said, “and the second is around clarity, of really asking landlords to be crystal clear in the reason why they’re asking someone to leave, and not necessarily limiting their ability to ask someone to leave but make sure there’s a written reason in paper.”

City Councillor Frank Baker told members of the Columbia-Savin Hill Civic Association that he was not comfortable with the bill as presented. He felt that the same rules should be applied to all landlords, regardless of size, and focus strictly on notification and a tenant bill of rights.

“I think the way it’s set up, in this eight-page document that everybody in this room would have a different opinion on,” Baker said, “it leaves itself wide open for lawyers to go into housing court.”

The council on Wednesday recommended that the matter be sent into working sessions and potentially another hearing before any action is taken.

“The hearing was very fair. It was objective, well-balanced,” said City Councillor Michael Flaherty, chair of the Government Operations committee. “We heard from a variety of proponents, opponents, advocates, and industry folks who provided their thoughts and suggestions on the legislation, and based on that and that we’ve endured lots of calls, meetings and email to our office asking that that matter remain in the committee with an eye toward a working session.”