Bethesda-based Lockheed Martin said Friday that it will furlough about 3,000 employees next week due to the government shutdown and expects that number to grow if the budget standoff doesn’t end soon.

The figure represents a fraction of the company’s roughly 120,000 employees but reflects a growing concern among contractors about Congress’s failure to reach an agreement to fund the government. Private companies have had more flexibility in the early days of the shutdown, but contracting executives have warned that the situation will soon worsen.

In a memo to employees, Marillyn A. Hewson, Lockheed’s chief executive, said affected employees should use vacation time and floating holidays so they can continue to be paid during the furlough. Those without enough vacation time will be given an advance on up to 40 hours of their salary, she said.

“If the shutdown extends beyond available vacation time, employees will be transitioned to unpaid furlough leave,” Hewson wrote. The company declined to say how many of the furloughed employees are based in the Washington area.

Hewson warned that Lockheed, the world’s largest defense contractor, expects the number of affected employees to increase “as we experience contractual actions and the impact of furloughs among” government inspectors.

The Aerospace Industries Association, an industry group, said in a statement Friday that othermember companies will have to furlough employees if the shutdown continues.

The pressing problem, the AIA said, is the shutdown’s effect on the Defense Contract Management Agency, which oversees contract performance. Without these inspectors, companies can’t continue work on some projects, the group said. 

United Technologies announced this week that the absence of DCMA inspectors will force it to halt some manufacturing work. The Hartford, Conn.-based company said that starting Monday its Sikorsky Aircraft unit will furlough nearly 2,000 workers — at facilities in Stratford, Conn., West Palm Beach, Fla., and Troy, Ala.

If the shutdown continues through next week, the company added, its Pratt & Whitney and aerospace systems units would also take action, potentially furloughing an additional 2,000 workers.

David F. Melcher, chief executive of McLean-based defense contractor Exelis, said this week that the shutdown’s toll on contractors would expand considerably as time goes on.

“Shutting down for a day or two is not going to be that much of an impact,” Melcher said. But “I think there is a definite and real impact if the shutdown lasts more than a couple weeks — for every company in this industry.”

Some contractors still haven’t announced how they will respond to an extended shutdown. BAE Systems’ Arlington-based U.S. business has said that it would pay its workers through the early days of the shutdown.

In a memo to employees Monday, before the shutdown began, Linda Hudson, the company’s chief executive, said that for the first week, “at least, pay and benefits for BAE Systems employees will not change.”

But a BAE spokesman declined to comment Friday on whether the company could begin furloughs next week.