In a sign that not every Trump official is on the same page, leaders at the FBI and State Department instructed employees not to respond.

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.

In an email, Elon Musk told hundreds of thousands of federal workers they have until just before Tuesday to explain what they accomplished over the last week. Some departments told employees not to respond.