Airline executives and government officials are working out plans to ease lengthy waits for Afghan refugees once they land in the U.S., people familiar with the discussions said.

The Pentagon this week began using U.S. airliners to carry people fleeing Afghanistan from Qatar, Germany and Bahrain in hopes of easing crowded conditions at those overseas bases. The effort quickly created a new bottleneck at Dulles International Airport near Washington, D.C., where flights have started arriving, with planes stacking up on the tarmac in some cases for hours before passengers have been allowed to disembark.

Airline executives, including American Airlines Group Inc. Chief Executive Doug Parker, United Airlines Holdings Inc. Chief Executive Scott Kirby, and Atlas Air Worldwide Holdings Chief Executive John Dietrich raised concerns with federal officials about the problem this week, including Thursday in conversations with Homeland Security Secretary Alejandro Mayorkas and other officials, according to some of the people.

United has made its hangar at Dulles available as an area where passengers can wait to be processed, these people said. American Airlines is working to set up a space to accommodate people before clearance at Philadelphia International Airport, where flights will soon start arriving. Other locations including New York, Chicago and Houston have also been considered, the people said.

Some flights arriving this week have waited after landing for 10 to 12 hours for clearance from U.S. Customs and Border Protection, on top of already long flights from overseas. The problems continued with more extended waits overnight Thursday. The situation started to improve Friday, with passengers from three flights disembarking within two hours, industry and government officials said.

The Department of Homeland Security didn’t respond to a request for comment.

The long waits for vetting passengers both before flights take off and after they land have created logistical headaches for airlines, as there are federal limits to how long crews can work before they must be allowed to rest. Some flights from overseas bases where evacuees are being housed to the U.S. have had to be scrubbed because crews were unable to fly, industry and government officials said.

Workers have been bringing in supplies like food, water and diapers as planes full of passengers waited. On one American Airlines flight, the crew ordered 50 cheese pizzas, the company said. Companies including Walgreens Boots Alliance Inc. have donated supplies for passengers—many of them families with small children—who hastily boarded evacuation flights with almost no personal belongings.

The union that represents flight attendants at United and Hawaiian Holdings Inc., another airline operating the flights, cautioned members Thursday to prepare for “long duty days, intense conditions onboard, and unanticipated operational delays on arrival.” The union suggested flight attendants pack water, wipes, gloves, masks and other supplies.

White House press secretary Jen Psaki said Friday that evacuees must undergo thorough vetting before they arrive. Additional layers of checks, including checking manifests and resolving issues, have at times led to delays on planes, she said.

"Ensuring that people are treated humanely as they are coming to the United States, they have access to food and to water, is something we are committed to, and we will continue to improve any of these conditions, but I think the reason why these planes are waiting is also an important part of the context here,” Ms. Psaki said.

—Michelle Hackman contributed to this article.

Write to Alison Sider at alison.sider@wsj.com and Andrew Tangel at Andrew.Tangel@wsj.com