Boeing has urged airlines to inspect all 737 Max airplanes for a possible loose bolt in the rudder-control system after an international airline discovered a bolt with a missing nut while performing routine maintenance, the Federal Aviation Administration said on Thursday.

After the international airline, which the agency did not name, noticed the missing nut, Boeing discovered that an undelivered 737 Max also had a nut that was not properly tightened, the F.A.A. said.

Boeing said it has delivered more than 1,370 of the aircraft worldwide since 2017 and has urged that all of them be inspected for the possible loose hardware. The company said it was also inspecting its undelivered 737 Max airplanes.

“The issue identified on the particular airplane has been remedied,” Boeing said in a statement. “Out of an abundance of caution, we are recommending operators inspect their 737 Max airplanes and inform us of any findings.”

The F.A.A. said it was closely monitoring the inspections and would consider further action if additional instances of loose or missing hardware were discovered.

Boeing said there had been no “in-service incidents” caused by possible loose hardware and that, before pushing back from the gate, flight crews routinely conduct checks that would alert them if the rudder was not working properly.

Such inspections involve removing an access panel and visually confirming that the bolt in the rudder-control system has been properly installed, Boeing said. The company added that the inspections would take about two hours per plane.

Several major American air travel companies, including United Airlines, Southwest Airlines, American Airlines and Alaska Airlines, use the 737 Max, a single-aisle workhorse aircraft built for short and intermediate distances.

United, American, Southwest and Alaska each said they did not expect the inspections would affect their operations. Alaska said it would begin the inspections on Thursday and expected to complete them in the first half of January. Southwest said it was carrying them out during routine overnight maintenance.

The 737 Max has a deeply troubled history.

In 2018, one of the planes, operated as Lion Air Flight 610, crashed into the ocean off the coast of Indonesia, killing all 189 passengers and crew members aboard. Less than five months later in 2019, another, operated as Ethiopian Airlines Flight 302, crashed shortly after leaving Ethiopia’s capital, Addis Ababa, killing all 157 people on board.

Regulators around the world grounded the Max after the second crash. The F.A.A. cleared it to fly again in late 2020 after Boeing made changes to the plane, including to M.C.A.S., the flight control system behind the crashes. The company said in late 2019 that it had fired its chief executive, and it agreed to a $2.5 billion settlement with the Justice Department in 2021.

Last year, Boeing reached a $200 million settlement with U.S. securities regulators, resolving an investigation into claims that the company and its former chief executive had deceived investors about problems with the 737 Max that led to the deadly crashes.