The New Orleans Civil Service Commission on Monday unanimously approved a proposal by Mayor Mitch Landrieu to raise all New Orleans Police Department officers’ pay by 10 percent over the next year, a move that drew relatively rare, and enthusiastic, support from all sides.

The good cheer didn’t last. The meeting soon broke down into bickering over a much thornier pay issue: how to compensate city firefighters who have been filling in for their superiors — in some cases for months or more — without receiving higher pay.

The 10 percent police raise, if approved by the City Council as expected, will be phased in between this summer and early next year. One 5 percent increase will take effect in July and another in January. Landrieu sought the raise after the city found that its 2014 revenue would be $14.6 million above projections, partly due to better-than-expected sales and property tax collections.

It will come on top of a 5 percent increase added to this year’s budget, a net increase of nearly 16 percent for officers who started with the department prior to this year. Overall, the city’s police officers will be among the highest paid in the state, Landrieu administration officials have said. The administration hopes the raise will help stem the flow of officers out of the department. Earlier this month, WWL-TV reported that the Police Department had 1,144 officers, about 400 fewer than when Landrieu came into office in 2010.

“We’re happy to support an increase to the pay plan for New Orleans police officers. It is badly needed,” said Donovan Livaccari, an attorney who represents the Fraternal Order of Police, the city’s largest officer group.

“Any opposition?” Commissioner Ron McClain said, drawing laughter from the crowd. “I enthusiastically move” for a vote.

While supportive, Nick Felton, president of the New Orleans Firefighters Association, was quick to insert a few words of criticism for the administration during his remarks on the raise.

“The best-paid police department in the state of Louisiana. Kudos. And just to give you an update, the firefighters are far, far, far below,” Felton said.

The remark served as a preview for the rest of the meeting.

The Civil Service Department staff, Felton and the Mayor’s Office have been trying for months to negotiate a solution on how to pay firefighters who fill in for superiors, as they’re required to do, but have only received their regular pay for the work.

In March, the Civil Service Department released a report that identified thousands of instances of these work arrangements and recommended that lower-ranking firefighters be paid at the higher positions’ rates for those hours. The city is willing to do that from now on, but Fire Department Chief Tim McConnell, during the March commission meeting, balked at making the change retroactive, which could cost the city hundreds of thousands of dollars. And an attorney for the city questioned whether the employees were even eligible for the additional pay under the city’s Civil Service Rules.

The firefighters’ union, the Civil Service Department and the Mayor’s Office were supposed to have made some progress on the issue, but they have only met once to discuss it in the past month. The meeting took place on Friday.

The city’s rules set a relatively high bar for when such employees must receive a higher rate of pay. They must work in the position for five full days in a single year and the higher position must be a “budgeted vacancy,” meaning it was supposed to be filled but wasn’t. In Jefferson Parish, the only requirement is that an employee must work one hour in a higher classification.

Felton has proposed changing the city’s rules to shorten the minimum time worked to two hours. But Alexandra Norton, a top Landrieu aide, said the administration favored a technical fix to the city’s payroll system. A change to the rules would require extensive review, a commission vote and a City Council vote, she said.

“If we go the route of revising the rule, it will be several months in the making,” Norton said at the meeting on Monday.

Civil Service staff member Robert Hagmann said the department’s analysis found a number of “budgeted vacancies” being filled by lower-ranked firefighters. But the mayor’s office has thus far failed to provide its own analysis for guidance, he said.

“You have to meet again. And I would suggest you not wait until the day before — the last business day before — the Civil Service Commission meeting,” McClain said, leading to an argument over which party was responsible for the last-minute meeting.

Norton said that she had unsuccessfully tried contacting city Personnel Director Lisa Hudson weeks ago to schedule a meeting. Hudson, for her part, said Norton and the Mayor’s Office stalled.

“Ms. Norton, you’re not telling the truth,” Felton said during the exchange.

Commissioners said they weren’t interested in the argument but in resolving the problem. Commissioner Tania Tetlow was particularly concerned about the retroactive pay debate, and said the commission shouldn’t leave it on the table for much longer.

“We need to vote on this next month,” she said.