The Trump administration has privately demanded that the University of Virginia oust its president to help resolve a Justice Department investigation into the school’s diversity, equity and inclusion efforts, according to three people briefed on the matter.

The extraordinary condition the Justice Department has put on the school — one of the nation’s most prominent public universities — demonstrates that President Trump’s bid to reorder the political structure of academia is more intense and far-reaching than has been previously understood.

The administration’s attempt to assert federal influence over state university leadership decisions also shows how Mr. Trump’s political appointees continue to wield the Justice Department’s investigative powers to achieve policy goals long sought by a top Trump adviser, Stephen Miller.

The Justice Department has contended to the university that the president, James E. Ryan, has not dismantled the school’s diversity, equity and inclusion programs and misrepresented the steps taken to end them. A spokesman for the department did not immediately return a request for comment.

The demand to remove Mr. Ryan was made over the past month on several occasions by Gregory Brown, the No. 2 official in the Justice Department’s Civil Rights Division, to university officials and representatives, according to the three people briefed on the matter.

Mr. Brown, a University of Virginia graduate who, as a private lawyer, sued the school, is taking a major role in the investigation. He told a university representative as recently as this past week that Mr. Ryan needed to go in order for the process of resolving the investigation to begin, two of the people said.