Whether Mr. Barr ends up relaying a redacted version of Mr. Mueller’s report or instead writes his own, he most likely will have to keep grand jury testimony secret.

He also may withhold classified information that could reveal intelligence sources and methods still being used to spy on the Russian government, like any moles or wiretaps.

Mr. Barr also noted that the Justice Department typically keeps confidential so-called declination memos where prosecutors explain what they uncovered about anyone they decide not to prosecute.

On Wednesday, Mr. Kinkopf noted that the Justice Department had taken the position that sitting presidents could not be indicted while in office. If Mr. Barr strictly enforces the view that department policy forbids putting out negative information about people whom prosecutors declined to charge, he said, that would prevent Justice Department officials from releasing information about Mr. Trump’s actions.