Attorney General Jeff Sessions asked all 46 of the U.S. attorneys appointed by former President Barack Obama who are still in their posts—including New York’s Preet Bharara, one of the nation’s highest-profile federal prosecutors—to submit their resignations on Friday.

The move appeared to backtrack on an earlier request by President Donald Trump that Mr. Bharara, the U.S. attorney for the Southern District of New York, remain in his job. Mr. Bharara is well-known for his aggressive prosecutions of insider trading and public...