Mr. Neal’s decision follows a shake-up at the Executive Office for Immigration Review, the court system that adjudicates the country’s immigration cases, including asylum cases. It is part of the Justice Department, not the judicial branch.

Three of its senior career officials — MaryBeth T. Keller, the chief immigration judge; Jean King, the general counsel; and Katherine H. Reilly, the deputy director — all left their roles this summer. Ms. King stayed at the immigration office in a different post.

Mr. Neal’s departure also comes amid the backdrop of the Trump administration’s efforts to curb both illegal and legal immigration, which have taxed the immigration courts, the criminal courts and border patrols along the nation’s southwestern border and prompted long-running discontent among immigration judges that they are being used to expedite deportations.

As Mr. Trump has sought to suppress immigration and cut down on the number of people who claim asylum in the United States, he has notched two wins at the Supreme Court.

On Wednesday, justices said in an unsigned order that amid an ongoing legal battle, the administration could bar most Central American migrants from seeking asylum in the United States if they passed through another country and were not denied asylum there. That decision will allow the administration to effectively bar migration across the southwestern border by Hondurans, Salvadorans, Guatemalans and others who must travel through other countries to get to the United States.