Disgruntled travelers across the US will face more disruptions to their plans this weekend, as airlines cancel hundreds of additional flights and delays continue to mount due to air traffic controller staffing shortages amid a government shutdown with no end in sight.

Flight cancellations across the U.S. could rise to 15%—or even 20%—if the government shutdown continues, Transportation Secretary Sean Duffy said.

Sean Duffy, the secretary of transportation, said on Friday that the mandate could reach as high as 20 percent at some airports if the shutdown continued to push air traffic controllers to look for o...