That has prompted concern among Mr. Trump’s advisers that Mr. McGahn’s statements could help serve as a key component for a damning report by the special counsel, Robert S. Mueller III, which the Justice Department could send to Congress, according to two people familiar with the discussions.

Mr. Trump’s lawyers realized on Saturday that they had not been provided a full accounting after The New York Times published an article describing Mr. McGahn’s extensive cooperation with Mr. Mueller’s office. After Mr. McGahn was initially interviewed by the special counsel’s office in November, Mr. Trump’s lawyers never asked for a complete description of what Mr. McGahn had said, according to a person close to the president.

Mr. McGahn’s lawyer, William A. Burck, gave the president’s lawyers a short overview of the interview but few details, and he did not inform them of what Mr. McGahn said in subsequent interactions with the investigators, according to a person close to Mr. Trump.