Air traffic staffing shortages were disrupting air travel around the nation Tuesday for a second consecutive day, with delays at airports in Nashville and Chicago.

The disruptions came a day after the transportation secretary warned that the government shutdown could lead to delays and cancellations, but neither the cause nor the severity of the shortages was immediately clear. The Federal Aviation Administration said in an advisory that air traffic control facilities in Philadelphia, Las Vegas, Nashville, Chicago, Houston and Boston were short-staffed.

The F.A.A. slowed traffic at Nashville International Airport, where a ground stop caused delays of more than two hours, and at O’Hare International Airport in Chicago, where incoming flights were delayed by 40 minutes.

In a statement posted online, the Nashville airport said that controllers would rely on radar systems from the airport tower Tuesday night because of “insufficient staffing” and that the en route center in Memphis — more than 200 miles away — would take over approach control later in the evening.

“Passengers, expect delays,” the statement said. “Pilots, have patience.”

Representatives for the F.A.A. and the Department of Transportation did not immediately respond to a request for comment about the nature or volume of the staffing shortages that had caused the delays. A spokesman for the controllers’ union directed inquires to the F.A.A.

The national air space has long been reeling from a staffing crisis among air traffic controllers, as the F.A.A. grapples with a shortage of about 3,000 controllers.

Earlier Tuesday, the controllers’ union released a statement saying that “it is normal for a few air traffic controllers to call in sick on any given day, and this is the latest example of how fragile our aviation system is in the midst of a national shortage of these critical safety professionals.”

Air traffic controllers are required to work without pay for the duration of a shutdown, though a 2019 law ensures they will be compensated when it ends. Controllers haven’t yet missed a paycheck because of the shutdown and are expected to collect a partial paycheck later this month, according to union officials.

Union officials have insisted that there is no organized effort among the country’s nearly 11,000 certified controllers to protest the shutdown by not showing up to work, and leaders have publicly warned their members that such actions would be unlawful.

On Monday, flights into airports serving New York, Denver and the Los Angeles area were delayed, hours after Sean Duffy, the transportation secretary, said that the F.A.A. would institute delays and closures if air traffic controllers failed to show up for work. Mr. Duffy said on Monday that there had been a “slight tick-up” in sick calls since the shutdown began.

During staffing shortages, the F.A.A. will closely monitor demand volume and adjust arrival and departure rates to ensure safety, said Michael McCormick, a professor of air traffic management at Embry‑Riddle Aeronautical University.