A rift appeared to open Sunday between some of President Donald Trump’s agency heads and Elon Musk, the billionaire tasked with reforming the federal government, over Musk’s demand that all federal employees state their weekly accomplishments or risk termination.

The F.B.I. director, Kash Patel, the director of national intelligence, Tulsi Gabbard, and others told employees not to respond to a directive from Mr. Musk to summarize their accomplishments.

Multiple major agencies, including the FBI, State Department and Pentagon, have directed employees not to respond to Musk’s email.

The American Federation of Teachers, a union representing more than 1.8 million educators, had sued to keep members of Mr. Musk’s government efficiency team out of the Education Department’s systems.