Officials at the department believe that the conservatives have now gone too far with document requests related to continuing investigations that the lawmakers clearly do not support, including the inquiry led by the special counsel, Robert S. Mueller III, into Russia’s election interference. A former federal law enforcement official familiar with the department’s views said that Mr. Rosenstein and top F.B.I. officials have come to suspect that some lawmakers were using their oversight authority to gain intelligence about that investigation so that it could be shared with the White House.

Mr. Trump’s threat on Wednesday to intervene bolstered those voices and could undermine the Justice Department’s ability to protect some of its most closely held secrets. Lawmakers conducting oversight are usually given summaries of the information, but not the intelligence collected directly from wiretaps and sensitive sources.

Similar standoffs between law enforcement officials and Congress have resulted in compromise dating back decades, but in those cases, the Justice Department had the support of the president. Without Mr. Trump’s support, Congress is gaining the advantage.