Boeing said Thursday that production and delivery of a “significant number” of its 737 Max planes could be delayed because of questions about a supplier’s work on the fuselages.

Boeing said the supplier, Spirit AeroSystems, used a “non-standard manufacturing process” during installation of fittings near the rear of some 737s. Aircraft parts must be produced and installed to meet exacting federal standards.

The company said the situation is not an immediate safety issue and planes already flying “can continue operating safely.” But, Boeing said, it notified the Federal Aviation Administration about the matter and is working to inspect planes and replace fittings when necessary.

The FAA said that “based on the facts and data Boeing presented, the FAA validated the company’s assessment that there is no immediate safety issue.”

The parts issue is the latest setback for Boeing. All Max planes were grounded worldwide for nearly two years after a pair of deadly crashes, and production flaws halted deliveries of the larger 787 jetliner several times in the past three years.

A Boeing spokeswoman said Thursday that the company could not say exactly how many planes are affected because the issue was just discovered.

Spirit provides fuselages for all Max jets, but it is not the only supplier for the fittings. For that reason, production of one model, the Max-9, is not affected by the current situation.

Shares of Arlington, Virginia-based Boeing fell more than 4% and Spirit tumbled more than 7% in after-hours trading.