WASHINGTON (Reuters) -Major airlines braced for a third day of government-mandated flight cuts Sunday after rising air traffic control staffing shortages snarled thousands of flights on Saturday.

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. 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.

Reductions in flights are mandated to reach to 6% on Tuesday and then hit 10% by November 14.

The FAA said on Saturday there were air traffic control staffing shortages 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.

Some 1,550 flights were canceled and 6,700 flights were delayed on Saturday, compared with Friday when 1,025 were canceled and 7,000 were delayed.

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 Sunday.

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

U.S. Transportation Secretary Sean Duffy said it was possible he could require 20% cuts in air traffic if more controllers stop showing up for work. "I assess the data," Duffy said. "We're going to make decisions based on what we see in the airspace."

Republican Senator Ted Cruz 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.