Threatening to curtail the pay of any controller who did not go back, Trump said he would award those who have not taken time off during the 41-day shutdown $US10,000 bonuses and would welcome the resignations of the rest.
"All Air Traffic Controllers must get back to work, NOW!!! Anyone who doesn't will be substantially 'docked,'" Trump wrote on social media. "REPORT TO WORK IMMEDIATELY."
The shutdown, the longest in US history, has forced 13,000 air traffic controllers and 50,000 Transportation Security Administration agents to work without pay. Some are absent as they work second jobs or cannot afford child care.
Some 20 per cent to 40 per cent of controllers have been absent on any given day at the 30 biggest US airports during the shutdown, the FAA said last week.
Airlines cancelled nearly 2000 flights on Monday, the fourth consecutive day cancellations have topped 1000 as government flight cuts and air traffic staffing absences continue to wreak havoc with aviation.
FlightAware, a flight tracking website, said 5825 flights were also delayed on Monday.
This followed almost 3000 cancellations and nearly 10,800 delays on Sunday, in the single worst day for flight disruptions since the government shutdown began on October 1.
A November winter storm in Chicago is also disrupting air travel.
The Federal Aviation Administration said it was suspending general aviation traffic at 12 airports with air traffic control staffing issues, including Chicago O'Hare and Reagan Washington National.
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.
The US Senate was drawing closer to a vote on legislation to end the shutdown on Monday.
In a procedural vote, senators advanced a House-passed bill that will be amended to fund the government until January 30 and include a package of three full-year appropriations bills.
If the Senate eventually passes the amended bill, the package still must be approved by the House of Representatives and sent to President Donald Trump for his signature, a process that could take several days.
The Federal Aviation Administration instructed airlines to cut four per cent of daily flights starting on Friday at 40 major airports because of air traffic control safety concerns.
Reductions in flights are mandated to reach six per cent on Tuesday and then hit 10 per cent by November 14.
One big question for airlines is when the FAA will lift the government-required flight cuts.
Transportation Secretary Sean Duffy has said he first wants to see air traffic control staffing and safety data improve.
Even before the shutdown, the FAA was about 3500 air traffic controllers short of targeted staffing levels. Many had been working mandatory overtime and six-day weeks. Duffy has sought to retain controllers who could retire, speed hiring and undertake a $US12.5 billion overhaul of air-traffic control systems.
