Luigi Mangione is being prosecuted for murder by two agencies: the Department of Justice, which answers to President Trump, and the Manhattan district attorney’s office, which is led by the only prosecutor to convict President Trump.

Mr. Trump and the Manhattan district attorney, Alvin L. Bragg, are far from natural allies. And the high-profile case of Mr. Mangione, who is charged with killing a health care executive, could set their offices on a collision course.

When Mr. Mangione was arrested in December, before President Trump took office, the U.S. attorney’s office for the Southern District of New York said the state prosecution would occur first. But last week, Mr. Trump’s attorney general, Pam Bondi, signaled that the Justice Department might move quickly, saying that federal prosecutors would seek the death penalty for Mr. Mangione.

“The president’s directive was very clear: We are to seek the death penalty when possible,” Ms. Bondi said in an interview with “Fox News Sunday.”

Deliberations over whether to seek the federal death penalty can take a year or more in the Southern District and the Justice Department. Ms. Bondi’s swift announcement was all the more unusual given that Mr. Mangione has yet to be formally indicted in federal court.

Mr. Mangione’s case has become an arena for Ms. Bondi to show her commitment to the president. Her decision “is more political theater than anything else,” said Cheryl Bader, a law professor at Fordham University.

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