Mayor Mitch Landrieu’s administration will have another chance to hash out a plan to pay firefighters $75 million it owes them in back pay before a Civil District Court judge steps in.

City officials and representatives of the firefighters union told Judge Kern Reese on Thursday that they are scheduled to go into mediation later this month in an attempt to settle the pay issue and another long-running dispute over the funding of the firefighters’ pension system.

But Reese warned that the mediation had better show results. If not, he suggested, he would seriously consider a motion by the firefighters to hold city officials in contempt of court or order the Orleans Parish Sheriff’s Office to seize city property to pay off the debt.

“This court is prepared to do what it has to do, and that involves everything in the quiver,” Reese said.

The case, known as the longevity suit, has been moving through the court system for decades as the firefighters sought to force the city to pay them state-mandated raises that were never put into effect by the city. While firefighters have won judgments ordering the city to pay, those have been ignored and are difficult to enforce because the city enjoys protections that keep the courts from issuing orders on how it must spend its money.

The drawn-out history of the case, however, could mean it’s time to challenge that situation, Reese said.

“It might be time to test the waters again,” he said. “And if I write something the 4th Circuit (Court of Appeal) and the Supreme Court like, the law could change.”

The mediation is expected to have a broader scope than just the issue of back pay. The firefighters and the administration also have been fighting over funding for the pension plan, which is now nearly insolvent. Firefighters have sued the administration for failing to fund the plan for several years — a judgment that they won — while the administration has argued that significant changes need to be made to put the plan on a fiscally sustainable path.

It’s unclear whether the mediation will yield an agreement. Firefighters rejected plans to broker a deal on these issues earlier this year, in part because they would have had to give up some or all of their claims to past pension payments and back pay.

Reese told attorneys for the city and the union that he would be willing to participate in the mediation process.

Follow Jeff Adelson on Twitter, @jadelson.