United Technologies Corp., a supplier of helicopters and jet engines to the U.S. military, said an extended government shutdown would force furloughs of as many as 5,000 workers.

The company is poised to lay off about 2,000 Sikorsky Aircraft employees in Connecticut, Florida and Alabama on Oct. 7, according to a statement Wednesday. Work on Black Hawk helicopters slowed after Defense Department inspectors stopped work Tuesday, United Technologies said in the statement.

Another 2,000 workers would be furloughed at Pratt & Whitney, which manufactures engines for Lockheed Martin Corp.’s F-35 fighter jet, and at UTC Aerospace Systems, a maker of landing gear and flight control systems, if the shutdown lasts into next week, the company said.

The total “could exceed 5,000 employees if the government shutdown continues into next month,” United Technologies said in the statement. The Hartford, Connecticut-based company receives about 18 percent of its revenue from the government, Chief Financial Officer Gregory Hayes said Tuesday.