By Alison Sider

Top executives at major airlines including American Airlines Group Inc., Southwest Airlines Co. and United Airlines Holdings Inc. met Thursday with White House chief of staff Mark Meadows as the companies and their employees make a final push for more job-saving government aid.

Airlines agreed not to furlough or lay off employees through the end of September in exchange for $25 billion as part of a broad pandemic relief package last spring. They hoped the funds would see them through the worst of the crisis, but six months later, travel demand is still hovering at around 30% of last year's levels and airlines expect recovery to be rocky and slow.

The restrictions of the first round of aid expire at the end of the month. Unless they receive another infusion of cash, airlines have said they would furlough tens of thousands of workers starting Oct. 1.

President Trump and lawmakers in both parties have said they support providing another $25 billion in aid to airlines so they can keep paying all their workers through next March. But Congress has been unable to come to terms on a broader relief package that could include the airline funds, and time is running out.

Following the meeting, airline CEOs told reporters they believe the White House is supportive of reaching a deal to boost airlines.

"We're just here to plead with everyone involved to get to a Covid-relief package before Oct. 1," said American Chief Executive Doug Parker. He added, "We believe they're very much interested in getting to a deal, and we're going to continue to work now with the speaker as well, " referring to House Speaker Nancy Pelosi (D., Calif.).

Airline executives and industry lobbyists have grown more pessimistic as Democrats and Republicans in Congress have remained at an impasse over basic questions like the overall size of the next relief package. Mr. Meadows has said previously that the administration was looking into executive orders that could assist the industry, but details have been murky.

Mr. Meadows told reporters Thursday that the president is supportive of providing aid to the airline industry, but executive actions aren't ideal.

Asked how much money the airline industry needs, Mr. Meadows said $25 billion. "Compared to $1.5 trillion, it's a rather small amount of additional assistance that could potentially keep 30,000 to 50,000 workers on the payroll," he said, referring to the possible $1.5 trillion price tag for the next coronavirus relief bill.

Airlines and labor unions are continuing to plan for the possibility that no further aid is coming.

Southwest Airlines has said enough employees agreed to depart on their own that it won't need to furlough any this year. Delta Air Lines Inc. said this week that it had been able to save enough through voluntary departures, reductions in workers' hours and other measures that it won't cut any flight attendants, mechanics or other front-line workers, with the exception of pilots. Currently the airline is planning to furlough more than 1,900 pilots, though the company and the union are still discussing measures that could mitigate that figure.

United Airlines pilots are voting on whether to accept reductions in their work schedules, which translates into lower pay, in exchange for a guarantee that all their jobs would be safe until at least June. Union leaders endorsed the proposal Wednesday and members will vote at the end of this month, just days before the first swath of furloughs is due to go into effect.

"Hundreds of thousands of airline workers need the Cares Act extension, but with pilot furloughs just weeks away, we can't wait," Capt. Todd Insler, chairman of United's pilots union, said.

Write to Alison Sider at alison.sider@wsj.com