As the federal shutdown continues, U.S. flights will be reduced to "a trickle" in the run-up to the Thanksgiving holiday because of rising air traffic control staffing shortages, Transportation Secretary Sean Duffy said in remarks that aired on Sunday.

Major airlines were dealing with a third day of government-mandated flight cuts after thousands of delays and cancellations snarled traffic on Saturday. The shutdown, which has reached a record 40 days, has led to shortages of air traffic controllers who, like other federal employees, have not been paid for weeks.

"It's only going to get worse... the two weeks before Thanksgiving, you're going to see air travel be reduced to a trickle," Duffy said on CNN's "State of the Union" program.

Millions of people usually travel in the run-up to Thanksgiving, one of the most important U.S. holidays, which this year falls on November 27.

"Many of them are not going to be able to get on an airplane, because there are not going to be that many flights that fly if this thing doesn't open back up," Duffy said.

DAILY FLIGHTS CUT

The Federal Aviation Administration instructed airlines to cut 4% of daily flights starting on Friday at 40 major airports because of air traffic control safety concerns. Reductions in flights are mandated to reach 6% on Tuesday and then hit 10% by November 14.

The FAA on Saturday said air traffic control staffing shortages were impacting 42 airport towers and other centers and delaying flights in at least 12 major U.S. cities, including Atlanta, Newark, San Francisco, Chicago and New York.

A growing number of air traffic controllers have retired since the federal shutdown started on October 1, Duffy said. The FAA is 1,000 to 2,000 controllers short of full staffing, he told CNN.

"I paid experienced controllers to stay on the job and not retire," Duffy said. "I used to have about four controllers retire a day before the shutdown, ...now up to 15 to 20 a day are retiring."

Some 1,550 flights were canceled and 6,700 were delayed on Saturday, up from 1,025 cancellations and 7,000 delayed flights on Friday.

Airline officials privately said the number of delay programs made it nearly impossible to schedule and plan many flights and expressed alarm about how the system would function if staffing issues worsen.

The cuts, which began on Friday morning, include about 700 flights from the four largest carriers: American Airlines , Delta Air Lines, Southwest Airlines and United Airlines. The airlines are due to cancel about the same number of flights on Sunday.

During the government shutdown, 13,000 air traffic controllers and 50,000 security screeners have been forced to work without pay.

Duffy had earlier said he could require 20% cuts in air traffic if more controllers stop showing up for work.

Republican U.S. Senator Ted Cruz of Texas said he was told by the FAA that since the shutdown started pilots have filed more than 500 safety reports about mistakes made by air traffic controllers because of fatigue.