The City of Richmond is facing a $4.1 million deficit and likely will have to dip into savings to avoid being in the red when the books close June 30 on the current 2015-16 fiscal year.

That’s according to Lenora Reid, the city’s chief financial officer.

She expects Mayor Dwight C. Jones to seek permission from Richmond City Council to move money from savings to deal with the projected deficit, although the amount could be smaller by the end of the month.

Ms. Reid expects the request to be introduced at the council meeting on Monday, June 13.

The good news, she said, is that the deficit is far smaller than the $12.4 million gap she initially projected in October.

Still, the deficit is bad news for the city, which has relied on surpluses in recent years to help fill budget holes.

Extra revenue has helped improve the city’s financial picture, according to the third quarter financial report Ms. Reid presented to City Council’s Finance Committee last month.

The report shows the city benefited from higher payments from the state, better than expected receipts from real estate and personal property taxes and higher than expected earnings from public utilities.

Overall, Richmond’s general fund revenues for operations are expected to total $696.2 million, or $7 million more than the council approved in May 2015 for a $689.3 million budget.

However, rising expenditures have more than swallowed up the additional revenue, according to the report. Overall, the city will finish the budget year with about $700.3 million in expenses — also well above the council-approved budget.

Increased spending on public safety and public works are among the reasons.

For example, the city police and fire departments are spending more on overtime this year as the result of unfilled vacancies and collectively are expected to be about $3 million over budget by June 30.

The Sheriff’s Office also is projected to be $2.4 million over budget, largely due to increased costs to provide medical care to inmates.

The Department of Public Works also is projected to spend $2.1 million more than it was budgeted because of higher than expected costs for the new citywide recycling program, additional expenses related to the UCI Road World cycling championship held in Richmond last September and the heavy winter snows, the report states.