WASHINGTON — Having filled a Supreme Court vacancy, President Trump is turning his attention to the more than 120 openings on the lower federal courts. On Monday, he will announce a slate of 10 nominees to those courts, a senior White House official said, the first in what could be near monthly waves of nominations.

The White House counsel, Donald F. McGahn II, said the nominations were a vindication of a commitment Mr. Trump made during the campaign “to appoint strong and principled jurists to the federal bench who will enforce the Constitution’s limits on federal power and protect the liberty of all Americans.”

The administration continues to draw on lists of 21 potential Supreme Court nominees, put together with the help of the conservative Federalist Society and Heritage Foundation, that Mr. Trump issued during the campaign. But it is looking at other sources, too, the White House official said. Mr. McGahn, who has supervised the selection of the nominees, is looking for scholarly credentials and “intellectual boldness,” among other qualities, the official added.

Jonathan H. Adler, a law professor at Case Western Reserve University, said the appeals court picks on Mr. Trump’s list included “incredibly strong nominees” who were within the judicial mainstream and should “have an intellectual influence on their courts.”