Mayor Dwight C. Jones wants Richmond City Council to allow him to tap the city’s piggy bank to keep red ink from staining the city’s books.

The council is to consider the mayor’s plan to fill the projected $5.8 million deficit at its meeting Monday, June 27.

The deficit includes $1.9 million in costs for clearing a major snowstorm last winter. And while it is small, representing less than 1 penny per dollar in the city’s $708.2 million budget, it is embarrassing for the mayor as he heads to the end of his second and final term unable to develop the kind of economic growth and revenues to keep up with rising city expenses.

The mayor’s plan calls for mostly shifting money from savings to fill the deficit.

The goal: To ensure the city will be able to close its books on the 2015-16 fiscal year June 30 with revenues and expenses balanced as required by state law.

The projected deficit is based on information provided prior to last week’s severe thunderstorm, which could require additional funding shifts to cover the city’s cleanup costs.

City Councilman Parker C. Agelasto, 5th District, said he plans to vote against the mayor’s proposal to protest the administration’s decision to wait until the last minute.

“Essentially, the council has no choice, but to pass” the mayor’s plan to meet the June 30 deadline, he said. That’s not the way it should work, he said.

Under the city’s charter, City Council is empowered to control the city’s purse and needs to be more involved in monitoring revenues and spending during the year, he said.

Mr. Agelasto said he and Councilman Jonathan T. Baliles, 1st District, have introduced a resolution that would require the city administration to come to the City Council every three months “to make needed adjustments.” That would “more closely align agency budgets with their projected expenditures,” Mr. Agelasto said.

The council already requires the administration to submit financial reports every three months, but has not sought to force budget adjustments based on the information.

Along with the $1.9 million in extra expenses from the winter storm, the deficit is largely the result of increased spending by the police, fire and sheriff’s departments, particularly for overtime for officers and firefighters and unexpected extra expenses, such as medical care for jail inmates.

Under the mayor’s plan, $1.67 million of the deficit would be covered by higher than expected revenues and by shifting unspent funds from some departments that under-spent their budgets to those that went over budget. The rest, $4.1 million, would come from savings.

Richmond’s revenues actually grew by $6.67 million in the past 12 months, but $5 million was restricted because it came from the Governor’s Opportunity Fund for use in the development of Stone Brewery in Fulton, according to city Budget Director Jay A. Brown.

While the $5 million was not specifically identified in the city’s quarterly reports to the council, Mr. Brown said that money could only be used for “Stone Brewery and for nothing else.”