Mr. Barr said he had authorized “specific instances” of investigative steps in some cases. He made clear in a carefully worded memo that prosecutors had the authority to investigate, but he warned that “specious, speculative, fanciful or far-fetched claims should not be a basis for initiating federal inquiries.”

Mr. Barr’s directive ignored the Justice Department’s longstanding policies intended to keep law enforcement from affecting the outcome of an election. And it followed a move weeks before the election in which the department lifted a prohibition on voter fraud investigations before an election…

[Richard] Pilger, a career prosecutor in the department’s Public Integrity Section who oversaw voting-fraud-related investigations, told colleagues he would move to a nonsupervisory role working on corruption prosecutions.

“Having familiarized myself with the new policy and its ramifications,” he wrote, “I must regretfully resign from my role as director of the Election Crimes Branch.” A Justice Department spokeswoman did not immediately respond to a request for comment about Mr. Pilger’s message.