WASHINGTON—The White House has withdrawn the nomination of Elaine McCusker, a senior Pentagon official in line to become a deputy defense secretary and comptroller, after she clashed with the White House over the 2019 suspension of military aid to Ukraine, administration and congressional officials said Monday.

Ms. McCusker was nominated in November to be the Pentagon’s comptroller, and the Senate was poised to start work on her confirmation. But the White House pulled her nomination on Monday after concerns arose over her...