City councilors, in their first public comments on a proposed $68 million contract for Boston’s largest police union, voiced concerns Tuesday about the safety and health of the city and the police officers who log excessive overtime on the job.

At a Ways and Means Committee hearing Tuesday, the councilors questioned city and police officials about the Boston Police Department’s practice of ordering officers to work extra shifts and inquired about whether hiring additional officers would help reduce the toll and cost of police work.

“I’m concerned about the officers and their well-being,’’ said Councilor Timothy McCarthy. “[For] so many police officers, it’s a bit much on them and on their families.’’

The overtime discussion comes as the council prepares to vote Wednesday on a new agreement with the Boston Police Patrolmen’s Associationthat would give the union’s 1,500 members a 2 percent wage increase annually over the next four years. It also comes after the city released its annual earnings report, which revealed that more than 100 Police Department employees — including police officers, members of the command staff, and police detectives — earned between $70,000 and $124,000 in overtime pay in the 2016 calendar year.

Councilors based most of their questions on the proposed deal, reached after months of negotiations and without arbitration.

Addressing the council were the city’s chief financial officer, David Sweeney, city labor relations director Alexis Tkachuk, and Deputy Superintendent Steven Whitman, who handles police labor issues.

Boston police officers are allowed under their contract to work an extra 50 hours each week, for a total of 90 hours. Officers pull extra shifts to fill staffing shortage and guard special events such as the Boston Marathon and the New England Patriots’ championship victory parade. But many officers say overtime is often mandatory, the councilors said.

“Ninety hours is a long time during the week,’’ said Councilor Tito Jackson, who is running for mayor. “Most of us work long hours but most of us aren’t in a situation where folks could potentially shoot us.’’

Lieutenant Detective Michael McCarthy, in a phone interview after the meeting, said overtime and costs associated with it are inevitable in a city police department with more than 2,000 uniformed officers.

“Officer safety is at the forefront of everything we do,’’ McCarthy said. “If there is a way we can curtail the amount that an officer is forced to work we would certainly welcome that.’’

“But we live in a city where we have championship sports teams and a lot of events that have to be covered,’’ he added. “With that comes the need to staff with officers and often that is done with officers on overtime.’’

McCarthy said Police Commissioner William Evans is open to hiring more officers and looking for ways to curb overtime spending. He said officers can’t predict when crimes occur and must be prepared to respond. Staffing levels remain roughly the same, McCarthy said, despite a growing need.

“Public safety comes with a price tag,’’ he said. “We are always looking for more officers. But it comes down to money. It costs a lot of money to hire more police officers.’’

In the past, the cost of overtime has opened the Police Department to accusations of out-of-control spending. A 2015 audit ordered by the city found that the department had exercised “little control’’ over the process for assigning extra hours for officers.

The audit determined that between 2010 and 2014, overtime hours continued to rise in spite of increased staffing and an overall decrease in city crime.

To rein in spending, Mayor Martin J. Walsh’s administration ordered the police department to reduce its overtime hours by 10 percent from fiscal year 2015. The city went a step further by providing “meaningful overtime budgets’’ to public safety departments for the first time in decades. The city allocated $60 million for police overtime in the last budget.

But the 2015 audit said such reforms would have little effect on individuals working the most hours. And some officials said Tuesday that adding more officers would simply mean more officers working overtime.

Sweeney noted that overtime has decreased citywide by 2 percent and by 10 percent in the police department in the last fiscal year, saving about $9 million, which he said was more than “if we hadn’t made any reforms in overtime.’’

“We’re making some progress, moving in the right direction,’’ he said, adding that the city’s efforts were noted in its AAA bond ratings last week.

Councilor McCarthy noted that “forced overtime’’ has taken a toll on the city’s officers and said he wants to see more programs in the police department that focus on improving officers’ health.

“I’m concerned about public safety,’’ the councilor said. “And I’m concerned about the public safety of our officers.’’

Meghan E. Irons can be reached at meghan.irons@globe.com.