NEW YORK — The Federal Aviation Administration said the U.S. air traffic system will resume normal operations by Sunday after lawmakers rushed a bill through Congress allowing the agency to withdraw furloughs of air traffic controllers and other workers.

The FAA said Saturday that it had suspended all employee furloughs and expected its operations to be back to normal by Sunday night, a move that would bring the air traffic control system back to full strength a week after staff reductions began causing extra delays to flights across the country.

The furloughs for air traffic controllers were a result of $85 billion in across-the-board automatic spending cuts — or sequestration — that took effect March 1 and have cascaded across the federal government. The FAA had to cut $637 million as its share of the automatic cuts, and the furloughs were part of that effort. The flight delays that ensued were one of the most visible consequences of the sequestration cuts.

Concerned about the inconvenience that the delays were posing for travelers across the country, the Senate approved a measure late Thursday that would give the federal transportation secretary flexibility to shift as much as $253 million to the air traffic control system and return the air-traffic system’s staffing to full strength.

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The House approved the measure Friday as President Obama and congressional Democrats relented on their stand that the airport delays would be addressed only as part of a broader effort to reverse the across-the-board spending cuts.

Flight delays piled up across the country last week at some key airports as the FAA kept planes on the ground because there weren’t enough controllers to monitor busy air corridors. Cascading delays held up flights at some of the nation’s busiest airports, including New York, Atlanta, Baltimore, Washington Dulles, Los Angeles and San Francisco.

Things could have been worse. A lot of people who had planned to fly last week changed their plans when they heard that air travel might be difficult, according to longtime aviation consultant Daniel Kasper of Compass Lexicon.

“Essentially what happened from an airline’s perspective is that people who were going to travel didn’t travel,” he said. But canceled flights likely led to lost revenue for airlines. Even if they didn’t have to incur some of the costs of fueling up planes and getting them off the ground, crews that were already scheduled to work still had to be paid.

“One week isn’t going to kill them, but had it gone on much longer, it would have been a significant hit on their revenues and profits,” Kasper said.

The challenges probably cost airlines less than disruptions from a typical winter storm, said John Thomas, an aviation consultant with L.E.K. Consulting.

“I think the fact that it got resolved … has minimized the cost,” he said.

The budget cuts at the FAA were required under a law enacted two years ago as the government was approaching its debt limit. Democrats were in favor of raising the debt limit without strings attached so as not to provoke an economic crisis, but Republicans insisted on substantial cuts in exchange. The compromise was to require that every government “program, project and activity” — with some exceptions, such as Medicare — be cut equally.

The FAA had reduced the work schedules of nearly all of its 47,000 employees by one day every two weeks, including 15,000 air traffic controllers, as well as thousands of air traffic supervisors, managers and technicians who keep airport towers and radar facility equipment working. That amounted to a 10 percent cut in hours and pay.

Obama chided lawmakers Saturday over their fix for widespread flight delays, deeming it an irresponsible way to govern, dubbing it a “Band-Aid” and a quick fix, rather than a lasting solution to the sequester.

“Republicans claimed victory when the sequester first took effect, and now they’ve decided it was a bad idea all along,” Obama said, singling out the GOP even though the bill passed with overwhelming Democratic support in both chambers.

He scolded lawmakers for helping the FAA while doing nothing to replace other cuts that he said harm federal employees, unemployed workers and preschoolers in Head Start.

Material from The New York Times is included in this report.