Flight delays and cancellations continue to snarl US air travel for a third day as Transportation Secretary Sean Duffy warned air traffic will be “reduced to a trickle” if the US government shutdown continues.

More than 2,900 flights to, from, or within the US were cancelled and 8,600 delayed by late afternoon on Sunday, according to flight tracker FlightAware. The longest delays were reported in Newark, New Jersey – more than two hours on average.

In a hopeful sign, lawmakers are working on a possible deal to reach a compromise on government funding and end the shutdown, according to US media reports.

The Senate was scheduled to convene on Sunday in a rare weekend session.

Duffy warned the impacts on air travel will grow dire if they do not break the stalemate soon.

“You’re going to see air travel be reduced to a trickle,” he said on CNN on Sunday. He added that travellers trying to fly home for the Thanksgiving holiday later this month may not be able to get there.

“Many of them are not going to be able to get on an airplane, because there are not going to be that many flights that fly if this thing doesn’t open back up,” he said.

The Federal Aviation Administration (FAA) announced last week that it would be reducing air travel capacity by up to 6% this weekend and 10% by next weekend at 40 of the nation’s busiest airports. The cuts do not apply to international flights, but some airlines may choose to also cancel some of those flights, the FAA said.

Air traffic controllers, who are not being paid during the shutdown, are reportedly fatigued and not coming to work, triggering the reductions in air traffic allowances.

Duffy said Defence Secretary Pete Hegseth offered to have military air traffic controllers step in to help but he declined the offer because they are not certified to direct air traffic at the civilian airports.

Altogether, hundreds of thousands of federal workers are not being paid since the Government ran out of money on 1 October. Food assistance for low-income Americans also has been in limbo, with the administration agreeing to pay only half of monthly benefits.

Sunday marked the 40th day of the longest shutdown in history as Republicans and Democrats still have not agreed on a funding resolution to reopen the government.

The two parties have blamed each other for causing the impasse and for the travel disruptions.

The White House said on Friday that Democrats were “inflicting their man-made catastrophe on Americans just trying to make life-saving medical trips or get home for Thanksgiving”.

Meanwhile, on Saturday Senate minority leader Chuck Schumer accused Republicans of “playing games with people’s livelihoods”.

Democrats have refused to back any Republican spending plan unless money for health insurance subsidies be included, while Republicans want to provide funding for the government without anything else attached.

US President Donald Trump suggested over the weekend money should be sent directly to Americans to buy health insurance rather than to insurance companies.

Republican senators are working on a compromise package that could end the impasse with a vote to advance legislation possibly coming on Sunday.