Flights into airports serving New York, Denver and the Los Angeles area were delayed on Monday night because of shortages of air traffic controllers, hours after the transportation secretary warned that flying could be disrupted by the government shutdown.

The delays began in the late afternoon at Newark Liberty International Airport in New Jersey, where incoming flights were delayed nearly an hour on average, and at Denver International Airport, where arriving flights were delayed about 40 minutes.

Later in the evening, Hollywood Burbank Airport near Los Angeles reported average incoming delays of about two and a half hours, according to a Federal Aviation Administration advisory. The air traffic control tower that serves Burbank had no controllers working on Monday night, so management of incoming flights was being assumed by counterparts at Southern California Terminal Radar Approach Control in San Diego, one of the busiest air traffic facilities in the world.

The delays, which were caused by staffing shortages, according to the F.A.A. advisories, came not long after the transportation secretary, Sean Duffy, warned that air service could be disrupted by the government shutdown.

“If we think there’s issues in the airspace, we will shut it down,” he said. “We will close it down. We will delay.”

Air traffic controllers are required to work through the shutdown, but will only be paid retroactively when it ends.

As the 2019 government shutdown wore on, controllers at important facilities began calling in sick at high rates, contributing to widespread flight delays and bringing a swift end to that shutdown. On Monday, Mr. Duffy said officials had seen a “slight tick-up” in sick calls from controllers since the current shutdown began last week.

The Federal Aviation Administration slowed traffic at the three airports on Monday using a “ground delay program,” a traffic management tool in which the agency holds flights from departing other airports if they are headed for one with limited capacity.

The F.A.A. has issued many ground delays for Newark for staffing shortages and runway construction this year and also issues ground delays when airports are dealing with bad weather and other factors. Flights into Boston’s Logan International Airport were also delayed for much of Monday because of runway construction.

Mr. Duffy also said on Monday that a federal program that subsidizes flights to rural areas would run out of funding by Sunday unless the shutdown ended, threatening service.