Elon Musk has drawn inspiration from his 2022 takeover of Twitter with the tactic. His threat on social media of termination did not appear in an email to federal workers requesting the work summaries.

Elon Musk deepened the confusion and alarm of workers across the federal government Saturday by ordering them to summarize their accomplishments for the week, warning that a failure to do so would be taken as a resignation.

Shortly after Mr. Musk’s demand, which he posted on X, civil servants across the government received an email from the Office of Personnel Management with the subject line, “What did you do last week?”

The missive simultaneously hit inboxes across multiple agencies, rattling workers who had been rocked by layoffs in recent weeks and were unsure about whether to respond to Mr. Musk’s demand. Officials at some agencies, including the F.B.I. and the State Department, told their employees to pause responses to the email.

Mr. Musk’s mounting pressure on the federal work force came at the encouragement of President Trump, who has been trumpeting how the billionaire has upended the bureaucracy and on Saturday urged him to be even “more aggressive.”

In his post on X, Mr. Musk said employees who failed to answer the message would lose their jobs. However, that threat was not stated in the email itself.

“Please reply to this email with approx. 5 bullets of what you accomplished this week and cc your manager,” said the Office of Personnel Management message that went out to federal employees on Saturday afternoon. The email told employees to respond by midnight on Monday and not to include classified information.

The email was received by workers across the government, including at the F.B.I., the State Department, the Environmental Protection Agency, the Office of Personnel Management, the Food and Drug Administration, the Veterans Affairs Department, the Centers for Medicare & Medicaid Services and the Consumer Financial Protection Bureau, according to copies seen by The New York Times.

Some agency leaders welcomed Mr. Musk’s move. “DOGE and Elon are doing great work! Historic. We are happy to participate,” Ed Martin, the interim U.S. attorney for Washington, D.C., whom Mr. Trump has nominated to run the office on a permanent basis, wrote in a message to his staff.

But in a sign of the upheaval and the potential legal and security issues caused by the demand, officials at some federal agencies told their staff to hold off on responding and await further guidance.

Among them was Kash Patel, the new F.B.I. director. “The F.B.I., through the Office of the Director, is in charge of all of our review processes, and will conduct reviews in accordance with F.B.I. procedures,” Mr. Patel wrote in an email to staff obtained by The Times. “When and if further information is required, we will coordinate the responses. For now, please pause any responses.”

For rank-and-file workers, the latest move by Mr. Musk underscored a climate of instability and fear inside the government. One staff member at the National Institutes of Health, who spoke on the condition of anonymity out of fear of retaliation, said she was shocked by the message, which she said left her with a sick feeling in the pit of her stomach. When she found out more of the context, she said, she messaged a colleague: “They’re terrorizing us.”

As confusion and alarm spread on Saturday evening among workers over Mr. Musk’s demand, he said on X that there was a “low bar” to meet it.

“An email with some bullet points that make any sense at all is acceptable!” he said. “Should take less than 5 mins to write.”

In response to his threat of dismissal if workers did not comply, the American Federation of Government Employees, the largest federal employee union, said it would challenge any “unlawful” terminations.

Everett Kelley, the union’s president, accused Mr. Musk and Mr. Trump of showing “utter disdain” for federal employees.

“It is cruel and disrespectful,” he said in a statement, “to hundreds of thousands of veterans who are wearing their second uniform in the civil service to be forced to justify their job duties to this out-of-touch, privileged, unelected billionaire who has never performed one single hour of honest public service in his life.”

The union told workers that it “strongly believes” the Office of Personnel Management did not have the authority to direct employees in the manner of its emailed request and advised them to seek guidance from a supervisor.

The demands raised significant legal issues, experts said.