WASHINGTON — President Trump said on Friday that he would nominate William P. Barr, a skeptic of the Russia investigation who served as attorney general in the first Bush administration a quarter century ago, to return as head of the Justice Department.

Mr. Barr, 68, would become the nation’s top law enforcement official as Mr. Trump and his associates are under investigation by the special counsel, Robert S. Mueller III, for whether they conspired with the Russian government to interfere in the 2016 election and help elect Mr. Trump. Mr. Barr would oversee the inquiry as key aspects of it are coming to a close.

Known for his expansive vision of executive power, Mr. Barr has criticized Mr. Mueller for hiring too many prosecutors who donated to Democrats and has cast doubt on whether Trump campaign associates conspired with Russians. Mr. Barr has also defended Mr. Trump’s calls for a new criminal investigation into his defeated 2016 opponent, Hillary Clinton, including over a uranium mining deal the Obama administration approved when she was secretary of state.

His nomination comes at a time of more than usual turbulence in the Trump White House, where John F. Kelly, the president’s second chief of staff, is expected to end his stormy 16-month tenure as early as this weekend. Nick Ayers, the vice president’s chief of staff, is seen as a leading candidate to succeed Mr. Kelly, although Mr. Ayers has enemies on the White House staff and is not universally beloved by Republicans.