WASHINGTON, Nov 10 (Reuters) - Despite hopes the federal government shutdown could end this week, air travelers in the United States are still in for a rough few days of cancellations and delays nationwide before taking to the skies gets back to normal.

The Federal Aviation Administration instructed airlines to cut 4% of daily flights starting last week 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 Friday, November 14 -- and Transportation Secretary Sean Duffy has warned they could reach 15% to 20% if the shutdown does not end.

The government might reopen this week, if lawmakers agree to restore federal funding, but it is unclear when the flight cuts will be rescinded. On top of the mandated cuts, flyers must also contend with thousands of delays every day due to rising air traffic control absences.

The shutdown, the longest in U.S. history, has forced 13,000 air traffic controllers and 50,000 Transportation Security Administration agents to work without pay.

On Saturday and Sunday alone, more than 1.2 million U.S. airline passengers were impacted by air-traffic-related delays and cancellations.

When the shutdown ends, it could take several days or longer for air traffic to return to normal.

Chris Sununu, the former New Hampshire governor who heads Airlines for America, told CNN on Monday that there is still "a tough week ahead. The FAA still has mandated cancellations, ramping up over the course of the week."

But, he added, "Keep your holiday plans. The system is going to be up, running viable and resilient by Thanksgiving and Christmas."

WHAT WILL HAPPEN TO THIS WEEK'S FLIGHT CUTS?

One big question for airlines is when the FAA will lift the government-required flight cuts. Duffy has said he first wants to see air traffic control staffing and safety data improve before removing current targets.

The FAA said last week that 20% to 40% of air traffic controllers at the 30 largest airports are not showing up on any given day.

American Airlines AAL.O said on Monday that delays and cancellations due to air traffic control staffing at the weekend had impacted 250,000 customers.

The FAA has told the airlines that about 24 hours after the shutdown ends, they can get the controllers their back pay. But that does not mean absences drop immediately and all controllers come back to work right away.

WHEN WILL DELAYS START TO GO AWAY?

Airlines canceled more than 2,950 U.S. flights and delayed more than 11,200 on Sunday in the third day of government-mandated flight cuts.

The FAA-mandated flight cuts to the top 40 airports accounted for around 800 flights -- but major airlines ended up canceling more than twice that figure on Sunday due to fallout from air traffic control staffing issues.

Delays won't come to an end until air traffic controllers start getting paid again.

If the shutdown continues, air safety workers would miss another paycheck this week, leading even more to call in sick so they can take on second jobs, like driving for Uber or making deliveries for DoorDash, to make ends meet.

If it lasts two more weeks, it could affect travelers over Thanksgiving, one of the busiest air travel times of the year.

(Reporting by David Shepardson, Editing by Rosalba O'Brien)

((Chris.Sanders@thomsonreuters.com; +1 202-558-8254; Reuters Messaging: chris.sanders.reuters.com@reuters.net))