Layoffs could be looming in city government if overtime costs can’t be controlled, Mayor Byron W. Brown warned Friday.

The issue surfaced as Brown and several cabinet members reviewed Fire Department spending. Overtime in the department will likely be $1.9 million over budget when the fiscal year ends in June, spurring city officials to warn that cost overruns could trigger painful cuts.

New figures were released Friday showing that the Fire Department is on track to spend $10.7 million in overtime for the year.

Brown credited interim Fire Commissioner Garnell W. Whitfield Jr. with making headway in containing overtime since January. But Brown and Finance Commissioner Janet Penksa warned that unless costs are reined in, there could be future layoffs.

The city is facing a $24 million budget shortfall in the new fiscal year, and officials said it’s critical that overtime in all departments be vigorously controlled.

“If we’re not able to get a handle on [overtime] . . . there are going to be live bodies — people who have families, people who work hard — who will be put out on the street. Because we’re going to have to make some cuts,” Brown warned during a meeting of the CitiStat accountability panel.

He said the city is scrutinizing overtime in every department — not just the Police and Fire departments where overtime costs are typically highest.

Brown also raised concerns that sick time in the Fire Department topped 20,800 hours over the past 14 weeks — or about 3,000 hours per two-week pay period. While the mayor and other city officials said the vast majority of firefighters are conscientious public servants, Brown said the minority who are “playing games” are impacting city finances.

Penksa said financial pressures facing the city leave budget officials “struggling with the possibility of layoffs.” The city has seen pension and health insurance costs skyrocket at a time when it’s also facing cuts in state aid and other problems.

Penksa acknowledged that the $8.8 million that was budgeted for Fire Department overtime in this year was a fairly “conservative” sum that even the control board questioned. But she said city officials were operating on the premise that the hiring of 52 new firefighters last autumn would have had a greater impact on shrinking overtime costs.

Penksa said her criticism of skyrocketing overtime and abuses of sick leave in some firehouses has subjected her to public “heckling” by firefighters.

“I’m not going to let that hold me back,” she said.

She said the city has a duty to crack down on a minority of employees who “aren’t playing by the rules.”

Acting Corporation Counsel David Rodriguez said the city plans to send notices to all employees letting them know that they could face sanctions if they abuse sick time.

The fire union has long insisted that high overtime is the result of understaffing. As for claims by administration officials that some firefighters are abusing sick leave, union President Daniel Cunningham repeatedly has said that until the mayor proves such allegations, it’s merely rhetoric.