In its initial complaint, the department focused on Ronald Reagan National Airport, outside Washington, D.C., where the two companies own a combined 69 percent of takeoff and landing slots. It also listed more than 1,000 city pairs where the two airlines dominate the market.
The two airlines said in the joint filing with the district court in Washington, D.C., that they had tried to settle the case before the complaint was filed "and continue to believe there ought to be a realistic possibility of settlement."
Two sources told Reuters earlier this week that there had been little or nothing in the way of settlement discussions before the complaint was filed. A person familiar with the matter said that the companies had offered concessions to the Justice Department but declined to describe them.
(Read more: DOJ: No fast trial on airline merger)
The two sides have been at loggerheads over a trial date. The Justice Department initially asked for a February trial and then amended that to March. The airlines asked for a November trial.
The airlines complained about the proposed delay in a second filing on Wednesday in which they said that the Justice Department's proposed schedule would "place the merger at risk regardless of its competitive benefits."
In the joint filing on Wednesday, the two sides asked the judge to resolve the dispute at an initial scheduling conference set for Friday.
Companies generally push for expedited trials in merger challenges. Holding a deal together for months puts a strain on the parties because they are essentially in limbo, unable to merge and hampered in making independent long-range plans.
The case at the U.S. District Court for the District of Columbia is No. 1:13-cv-012346-CKK.