On Christmas Eve 1998, five days after the House impeached President Bill Clinton, Brett Kavanaugh urged his boss — Kenneth W. Starr, the independent counsel — not to pursue a criminal indictment of Mr. Clinton until after he left office.

Judge Kavanaugh, now President Trump’s nominee to fill the Supreme Court seat left vacant by the retirement of Justice Anthony M. Kennedy, delivered the advice in a private memorandum made public on Friday by the National Archives in response to a Freedom of Information Act request.

It shows that Judge Kavanaugh believed — rightly, it turned out — that the Senate would fail to convict the president for the “high crimes and misdemeanors” that Mr. Starr and Mr. Kavanaugh had enumerated for Congress after Mr. Clinton’s affair with Monica Lewinsky.

“After the Senate has concluded, I would send a letter to the attorney general explaining that we believe an indictment should not be pursued while the president is in office,” Judge Kavanaugh wrote. He urged Mr. Starr to close the independent counsel’s office, which had spent four years pursuing Mr. Clinton, so “the next president can decide what to do.”