Air travelers could face more frustration as busy U.S. airports need to meet a higher Federal Aviation Administration target for reducing flights Tuesday after already canceling thousands to scale back demands on the nation’s aviation system during the government shutdown.

Absences and signs of stress among traffic controllers, who haven’t been paid in over a month, made it imperative to cut flights in the name of public safety, the FAA said, ordering domestic airlines last week to drop 4% of their flights at 40 major U.S. airports. After already canceling more than 7,900 since Friday, the goal for cutting flights rose to 6% on Tuesday and again to 10% on Friday.

Nearly 1,200 flights were canceled Tuesday, according to FlightAware, a website that tracks air travel disruptions. It was unc

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