NEWARK/WASHINGTON (Reuters) -The Federal Aviation Administration will send investigative letters to airlines that did not comply with required flight cuts at 40 major airports prompted by air traffic control safety concerns during the government shutdown, the agency said on Monday.

"We will be sending out letters of investigation to any of the airlines who we don't feel lived up to the requirement to reduce capacity," FAA Administrator Bryan Bedford said at a news conference at Newark airport. "That's going to be an ongoing investigation."

Transportation Secretary Sean Duffy said airlines must comply with FAA orders. "If those airlines did not comply ... there should be accountability," he said at the event.

Major airlines did not immediately respond to requests for comment.

FAA officials originally aimed for a gradual increase in reductions to 10% of domestic flights at the 40 high-traffic U.S. airports, but they opted on Nov. 12 to freeze that requirement at 6% after disruptions declined dramatically as the federal shutdown came to an end. The FAA then dropped the required cuts to 3% before lifting them entirely on Nov. 16.

Data from Cirium, an aviation analytics firm, showed airlines repeatedly failed to comply with the flight cut requirements and on the final full canceled just 0.25% of flights at those 40 airports - less than normal cancellations - and far less than the 3% required.

The order said the FAA could seek a fine of up to $75,000 for every flight operated above the mandated limits.

The agency originally ordered flight cuts to minimize travel disruptions caused by shortages of air traffic controllers during the federal shutdown, when many of them stopped coming to work because they were not being paid.

The FAA is about 3,500 air traffic controllers short of targeted staffing levels. Many had been working mandatory overtime and six-day weeks even before the shutdown led to them working without pay.

Absences of air traffic controllers led to tens of thousands of flight cancellations and delays after October 1, when the shutdown began.