“When Mr. Benczkowski and fraud section lawyers met with Mr. Giuliani, they were not aware of any investigation of Mr. Giuliani’s associates in the Southern District of New York and would not have met with him had they known,” said Peter Carr, a department spokesman.

The Justice Department’s public statement on Sunday illustrates the unusual and broad set of roles that the president’s personal lawyer has played in the scandal that has engulfed the White House and imperiled Mr. Trump’s presidency.

Even as Mr. Giuliani ran a shadow foreign policy campaign to pressure Ukraine to investigate the president’s political enemies — which is now at the heart of an impeachment inquiry against Mr. Trump — he and his business associates were under criminal investigation for unlawfully wielding political influence. And while all of this was happening, Mr. Giuliani still served as a lawyer to clients with cases to plead before the Justice Department.

In distancing itself from Mr. Giuliani and trying to draw bright lines around how the Justice Department will and will not engage with him, the department has also undercut the perception that Mr. Giuliani can influence some of Washington’s most important lawyers and decision makers. That could make it harder for Mr. Giuliani to represent clients who are under Justice Department scrutiny in the future.

“This is an incredibly unusual statement from the Justice Department, which does not comment on ongoing investigations or even acknowledge them, and it’s the kind of statement that would give clients pause about who is representing them,” said Joyce Vance, a former federal prosecutor.