US President Donald Trump threatened on Monday to dock the pay of air traffic controllers he accused of shirking their "patriotic" duty, while their union decried being used as "political pawns" during the government shutdown.

The statements highlighted the mounting strains on the aviation industry as the record-long shutdown hits day 41, though a compromise bill advancing in Congress was raising hopes of an imminent resolution.

Thousands more trips involving US airports were cancelled or delayed on Monday after nearly 3,000 were cut a day earlier, according to tracking website FlightAware.

The Trump administration last week ordered 10-percent reductions in flights at dozens of airports, including some of the nation's busiest, due to concerns that staffing strains could threaten safety.

Air traffic controllers, who are already in short supply in the United States, have been working without pay in the shutdown, leading some to call in sick.

Trump took to social media on Monday to slam the absenteeism as un-patriotic, threatening that those who do not return to work "will be substantially 'docked.'"

"All Air Traffic Controllers must get back to work, NOW!!!" he demanded on his Truth Social platform.

Trump said he was recommending a bonus of US$10,000 to the "GREAT PATRIOTS" who did not take time off during the shutdown.

His statement was posted just as a press conference was concluding with the National Air Traffic Controllers Association (NATCA), organised to mark the second consecutive zero-dollar pay cheque for its members.

"Enough is enough," said NATCA president Nick Daniels. He called an emerging deal in Congress a "right step in the right direction."

"Air traffic controllers should not be the political pawn during a government shutdown," said Daniels, who has spoken in increasingly dire terms since federal funding first lapsed on October 1.

Democratic congressman Rick Larsen called Trump's comments "nuts."

"The women and men working long hours in air traffic control towers to keep the aviation system running deserve our thanks and appreciation, not unhinged attacks on their patriotism," said the Washington representative.

The prospects for a potential resolution to the longest shutdown in US history looked brighter on Monday, after enough Democrats in the US Senate crossed sides to advance a bill to fund the government through January.

However, Daniels noted that it took two and a half months after a lengthy shutdown in 2019 for all controllers to receive back pay. (AFP)