One is Justice Joan L. Larsen, a former law clerk to Justice Antonin Scalia and law professor at the University of Michigan, who now serves on the Michigan Supreme Court. She will be nominated to the United States Court of Appeals for the Sixth Circuit, in Cincinnati.

The other is Justice David R. Stras, a former law clerk to Justice Clarence Thomas and law professor at the University of Minnesota, who now serves on the Minnesota Supreme Court. He will be nominated to the Eighth Circuit, in St. Louis.

Justice Neil M. Gorsuch, Mr. Trump’s Supreme Court appointee, was on the campaign lists. So was Amul R. Thapar, a federal district court judge in Kentucky, Mr. Trump’s only nominee so far to the lower federal courts. Judge Thapar awaits a vote on his nomination to the Sixth Circuit.

Monday’s slate of nominees will be followed by additional ones at regular intervals, the White House official said.