However Nick Calio, head of Airlines for America which represents the major airlines, said the US Court of Appeals will most likely not hear the case until after the furloughs begins, the Associated Press reported.
Airline industry experts say if the cuts go into effect, they could create massive air travel delays for passengers across the country, which could "snowball" by Monday, CBS News said.
"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. "We think there is not one airport in the nation that will be immune to this."
Federal officials said they must furlough the FAA's 47,000 employees, including nearly 15,000 controllers, in order to cut $637 million from the budget by September. That, in effect, reduces the controllers' work by some 10 percent over the next few months.
"Air traffic controllers have never been furloughed, regardless of any budget cuts, and there is a reason for that--they are critical to maintain the safety and efficiency of the National Airspace System," Calio said in a statement.