Over 6,600 flights were delayed and more than 1,900 canceled in the United States on Sunday as the government shutdown’s impact on air travel grows more significant ahead of the holidays.

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 last week ordered flight cuts at the nation’s busiest airports as some air traffic controllers, who have gone unpaid for nearly a month, have stopped showing up fo...