American Airlines' Boeing 737 Max planes sit parked outside of a maintenance hangar at Tulsa International Airport (TUL) in Tulsa, Oklahoma, May 14, 2019.

The president of the pilots' union at American Airlines wants Boeing to give his safety experts time in a 737 Max flight simulator before the planes fly again.

Daniel Carey says it's essential that pilots who'll fly the plane be involved as it goes through re-certification by regulators.

Carey made the request Thursday to Boeing CEO Dennis Muilenburg. No U.S. airline has a Max simulator, but Boeing does.

Boeing didn't comment immediately.

About 400 Max jets around the world are grounded after crashes in Indonesia and Ethiopia killed 346 people. Boeing is updating flight-control software implicated in the accidents.

Pilot training — including whether to require time in simulators — has become a key issue as the Federal Aviation Administration and other regulators decide whether the planes can resume flying.