This contradicts guidance from some Trump administration officials that the request is voluntary.
The confusing back-and-forth has rippled through the federal bureaucracy, with some agencies instructing workers to comply and others not.
It has become a test of how much power Musk wields over the government's operations as he pursues an unprecedented cost-cutting campaign with President Donald Trump's backing.
Twenty-one workers resigned from his so-called Department of Government Efficiency in protest on Tuesday, saying they refused to aid the downsizing effort.
"We will not use our skills as technologists to compromise core government systems, jeopardise Americans' sensitive data, or dismantle critical public services," the employees wrote in a resignation posted online.
DOGE did not respond to a request for comment on the resignations.
The workers, who include data scientists, product managers and the division head of IT, were employed in an office known as the United States Digital Service before Musk took it over and renamed it DOGE after a favourite cryptocurrency.
The resignations added to the drama surrounding Musk's email demand, which was sent to employees across the government over the weekend asking them to summarize their accomplishments of the past week by Monday.
In a post on X, the social media site Musk owns, he asserted that failure to respond would constitute resignation.
With the deadline approaching on Monday, the Office of Personnel Management, the government's human resources arm, told workers they could ignore the email.
But Musk, the billionaire chief executive of Tesla and SpaceX, was undeterred.
"Subject to the discretion of the president, they will be given another chance. Failure to respond a second time will result in termination," he wrote on X late on Monday without setting a new deadline.
Prior to the new OPM guidance, Trump said workers who did not respond would be "sort of semi-fired," adding to the uncertainty.
Asked on Tuesday whether the renewed threat would be carried out against non-compliant employees, White House press secretary Karoline Leavitt told reporters that Trump would defer to cabinet secretaries' guidance for their individual workforces.
NEW FISSURES IN TRUMP ADMINISTRATION
The head-spinning developments exposed new fissures within Trump's administration over Musk's blunt-force approach. Even some Trump loyalists, such as Kash Patel, the newly installed FBI chief, told employees to hold off on replying.
Leavitt rejected any suggestion of rifts within the administration, saying everyone was "working as one team."
Musk will attend Trump's cabinet meeting on Wednesday to discuss DOGE efforts, she said.
Employees at several agencies said they received conflicting guidance from leadership, leaving them unsure how to proceed.
The Department of Health and Human Services advised employees that if they chose to reply, they should refrain from mentioning specific drugs or contracts, according to an email reviewed by Reuters.
"Assume that what you write will be read by malign foreign actors and tailor your response accordingly," the email said.
The head of the Small Business Administration, Kelly Loeffler, backed Musk's email requirement in a Fox News interview on Tuesday.
"We just want to know: Are there people there doing their jobs? I look forward to making sure that we get all the responses back, and for those that we don't, we'll have decisions to make."
The acting director of OPM itself sent an email to the agency's staff that said responding was voluntary "but strongly encouraged."
At the National Oceanic and Atmospheric Administration, the government's weather forecaster, a deputy on Monday instructed workers to email a form letter with generic accomplishments, a source told Reuters.
Musk's downsizing initiative has laid off more than 20,000 workers, with another 75,000 accepting buyouts, and the effort continued to accelerate on Tuesday.
IRS executives have been told to brace for another round of job cuts beyond the nearly 12,000 IRS employees already slated to be terminated, two people familiar with the matter said, referring to the roughly 7000 probationary employees set to be fired and 5000 employees taking a buyout. The cuts so far amount to more than 10% of the IRS workforce.
The executives were not told how many employees would be fired in the next round of layoffs only that they would be "aggressive," the sources said.
Gavin Kliger, the 25-year-old software engineer dispatched by Musk to scrutinise IRS operations, has told executives he believes the agency can meet its mission with computers and far fewer employees, the sources said.
OPM's acting head, Chris Ezell, published a memo on Tuesday requiring poorly performing managers to be fired and directing their superiors to evaluate them in part on how well they advanced the president's goals.
The vast majority of fired workers were in their jobs for less than a year, making them easier to lay off under civil service rules. But OPM has begun firing career workers within its own agency in what sources told Reuters is intended to serve as a template for a second round of mass layoffs across the government.
