It was unclear whether the president’s call on Thursday was an effort to explain his change of heart about keeping Mr. Bharara or to discuss another matter. The White House would not comment on Saturday.

However, there are protocols governing a president’s direct contact with federal prosecutors. According to two people with knowledge of the events who were not authorized to discuss delicate conversations publicly, Mr. Bharara notified an adviser to the attorney general, Jeff Sessions, that the president had tried to contact him and that he would not respond because of those protocols. Mr. Bharara then called Mr. Trump’s assistant back to say he could not speak with the president, citing the protocols…

Two White House officials, speaking on condition of anonymity to avoid offending the president, said the promise to keep Mr. Bharara on was a product of a chaotic transition process and Mr. Trump’s desire at the time to try to work with Senator Chuck Schumer, Democrat of New York, with whom Mr. Bharara is close. The relationship between Mr. Trump and Mr. Schumer, the Senate minority leader, has since soured.