Call it the big shrink at City Hall.

Mayor Dwight C. Jones and Richmond City Council have combined to eliminate funding for at least 379 vacant jobs, essentially positions funded by taxes paid into city coffers.

The wipeout of the money for the vacant jobs — amounting to nearly 10 percent of the city’s 3,853 authorized general fund positions — has provided $19.4 million to pay for other priorities. That’s based on an average cost per full-time position of $51,187 in wages and benefits, such as health insurance and retirement.

The use of vacancy savings — money left when authorized positions are not filled — is included in the amended city budget package for fiscal year 2016 that the council approved last Friday and that will go into effect July 1.

In all, the council approved $1.5 billion in spending for city operations, utilities and other aspects of the government, ranging from grants or special funds to city cemeteries and capital spending on streets, public buildings, parks and other public property.

The general fund portion of the budget — the part that largely relies on local tax revenue and covers city operations, the city’s contribution to public schools, public safety, courts and social services — provides about $689 million for FY16, or about the same amount being spent this year.

The council relied heavily on vacancy savings to provide for its top priorities — a 2.5 percent salary increase for police officers and firefighters currently on staff and an additional $9 million contribution for city schools — two items that were not funded in the mayor’s proposed budget.

Mayor Jones already had wiped out about 200 positions in order to present a balanced budget, and the council, over the objections of two members, eliminated another 179 positions. Council President Michelle R. Mosby, 9th District, and Kathy C. Graziano, 4th District, were the two opponents.

The Jones administration warned the council that permanently reducing the number of funded positions could force cuts in services, but the council’s action suggests that the mayor’s increasing status as a lame duck is reducing his influence. His current and final term will end in 18 months.

Richmond departments have long relied on vacancy savings to hire temporary and contract workers to get work done or to cover overtime costs. The decision to shrink vacancy savings means every department will have less money.

Even Richmond Police was not immune. It is to lose $1.1 million — or about 20 positions — in the fiscal year that begins July 1.

The Department of Public Works will take the biggest hit — nearly $2.2 million, or enough to hire 40 full-time employees. The department has relied on money from the funded but unfilled positions to hire temporary people to collect leaves, operate snowplows, repair alleys and collect tree limbs and other bulk trash.

Still, the impact of losing the vacancy savings remains a question mark, according to Selena Cuffee-Glenn, the city’s new chief administrative officer.

Ms. Cuffee-Glenn, who started Monday, echoed the mayor in saying she is “working with my team to determine what the effects will be on daily operations.”

“For me, the best way to ensure the delivery of services our residents expect and deserve is for the government to be efficient,” she said Tuesday in a telephone interview.

She said she and her staff would closely monitor spending in implementing the budget that the council approved.

In a statement released after approving the budget, Council President Mosby and her eight colleagues expressed confidence “that the mayor can manage this budget.”

The council also indicated that Mayor Jones always has the option to seek approval to dip into savings to “ensure significant services are not jeopardized.”

Mayor Jones, however, responded that he would not use city reserves to pay for services that the city no longer may be able to afford.

“I want to be clear: I do not support taking reserve funds to pay for ongoing operations,” the mayor stated after the council’s budget vote. “Such actions will only threaten our favorable bond ratings, which, if impacted, will represent a major step backward for our city.

The mayor also called the use of savings to pay for operations an “approach to budgeting that is neither advisable nor sustainable.”

Ms. Cuffee-Glenn said she agrees with the mayor and would seek to provide services using the funding that the council provided for operations.