BERLIN—German officials said a shipment of face masks destined for Germany was seized at Bangkok airport and diverted to the U.S. in an act of “modern piracy”—the latest accusation that the Trump administration is throwing its weight around in the global scramble to secure scarce protective equipment needed in the fight against coronavirus infections.

In March, Germany’s government accused President Trump of trying to persuade a local biotech firm in an advanced stage of developing a coronavirus vaccine to relocate its research...