WASHINGTON — Predicting a nightmarish air-travel snarl that will stretch from coast to coast, the airline industry and the nation’s largest pilots union joined forces Friday to sue the Federal Aviation Administration (FAA) over its decision to furlough air traffic controllers to achieve spending cuts required by Congress.

Two airline trade associations and the Air Line Pilots Association said they filed a lawsuit asking the U.S. Court of Appeals in Washington to stop the furloughs, which are scheduled to kick in Sunday. However, the earliest the court is likely to schedule a hearing is next week, after the furloughs have begun, said Nick Calio, head of Airlines for America, which represents major carriers.

The way in which the FAA has chosen to implement the furloughs could result in one of every three airline passengers across the country suffering flight delays or cancellations, industry officials said at a news conference. “The impact of these cuts on our industry cannot be overstated,” said Faye Black, vice president of the Regional Airline Association, which joined the suit.

Sunday is a light air-travel day, but by Monday the effects of the furloughs should start to “snowball,” creating an air-travel mess, said Lee Moak, president of the pilots union.

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Federal officials have said they have no choice but to furlough all 47,000 of the FAA’s employees, including nearly 15,000 controllers, if they hope to cut $637 million from the agency’s budget by the end of September, as required under automatic, across-the-board spending cuts imposed by Congress. Each employee will lose one day of work every other week, which will amount to a 10 percent reduction in available controller work hours to staff air-traffic facilities on any given day.

FAA officials declined to comment on the lawsuit.

The controller furloughs will save the agency $200 million, FAA Administrator Michael Huerta said this week. An FAA analysis released Thursday said fewer controllers will mean major delays at some of the nation’s busiest airports.

Maximum delays of more than three hours were predicted for some flights to Atlanta’s Hartsfield-Jackson International Airport, the world’s busiest airport as measured by the number of passengers who pass through it.

Other airports expected to experience significant delays as a result of the furloughs include Newark Liberty in New Jersey, John F. Kennedy and La Guardia in New York, O’Hare in Chicago, Los Angeles, Minneapolis-St. Paul, San Diego and Fort Lauderdale-Hollywood in Florida. Airports in Philadelphia, San Francisco, Miami and Charlotte, N.C., as well as Chicago’s Midway International Airport, are forecast to experience lesser delays.