WASHINGTON (Reuters) -Airlines canceled more than 2,700 U.S. flights on Sunday and Transportation Secretary Sean Duffy warned air travel will fall to a "trickle" in the run-up to the Thanksgiving holiday as air traffic control staffing shortages surge during the federal shutdown.

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.

Sunday's cancellations were the single worst day for flight cancellations since the shutdown began on October 1. 

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.

Many airlines have already planned their cancellations for the coming days. United Airlines, for example, will cut 190 flights on Monday and 269 on Tuesday, the company said.

As of 9:45 p.m. ET (0245 GMT) on Sunday, data from flight tracking site FlightAware indicated there had already been 2,762 U.S. flight cancellations and more than 9,900 delays as conditions looked to be worsening. The Federal Aviation Administration earlier in the day said it had staffing issues at 12 towers.

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 impact on air travel could hit U.S. economic growth, White House economic adviser Kevin Hassett said in an interview that aired on Sunday.

"Thanksgiving time is one of the hottest times of the year for the economy... and if people aren't traveling at that moment, then we really could be looking at a negative quarter for the fourth quarter," he told the CBS show "Face the Nation".

Airlines for America, which represents major carriers, said staffing issues had disrupted more than 4 million passengers' travel plans since October 1, when the shutdown began.

By next Friday, it estimated a daily U.S. economic impact of $285 million to $580 million.

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.

During the 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.