US President Donald Trump has demanded air traffic controllers return to work as travellers endured another day of flight cancellations, which the administration ordered to manage staff shortages during the government shutdown.

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

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