Mayor Martin J. Walsh has proposed rules that would require vendors with city contracts for custodial and building security services to pay their employees more — a potential salary boost for hundreds of workers.

The proposed changes, to be presented this week to the City Council, would require the vendors to pay the state prevailing wage of $14.85 to $20 per hour, along with an additional $6.06 to $6.70 in health and pension benefits through 2020.

Currently, those workers are guaranteed only Boston’s living wage rate of $14.82 per hour, as of July 1.

The proposal would apply to all custodial and security workers with private vendors in city-owned buildings, including, for example, guards at the Boston Public Library and custodians who work in City Hall. The current ordinance covers only vendors with more than 25 full-time employees and with contracts valued at $25,000 or more.

Walsh said in a statement that he was proud to be “leading by example in lifting up workers who provide critical services to our city and often times go unrecognized for their important contributions.’’

The proposal would also require new vendors to extend employment opportunities to workers who served under the previous contract — which Walsh said would provide stability for workers and consistency for city services.

Boston’s Jobs and Living Wage Ordinance on Wednesday will go before the City Council, which is likely to schedule a hearing on the proposal.

The original ordinance — one of the first in the country to require that workers on city contracts be paid a so-called living wage — is calculated for a family of four to live at or above the federal poverty level, city officials said. It’s recalculated every year, based on inflation and cost-of-living adjustments. It was set at $14.82 on July 1.

Walsh’s proposal follows new state legislation, signed into law by Governor Charlie Baker last month, that will mandate paid family medical leave and increase the state’s minimum wage, which will rise gradually over the next five years to $15 an hour, beginning in January.

Milton J. Valencia can be reached at milton.valencia@globe.com. Follow him on Twitter @miltonvalencia.