The prosecutors, Carey R. Dunne and Mark F. Pomerantz, submitted their resignations after the new Manhattan district attorney, Alvin Bragg, indicated to them that he had doubts about moving forward with a case against Mr. Trump, the people said.

Mr. Pomerantz confirmed in a brief interview that he had resigned, but declined to elaborate. Mr. Dunne declined to comment.

Without Mr. Bragg’s commitment to move forward, the prosecutors late last month postponed a plan to question at least one witness before the grand jury, one of the people said. They have not questioned any witnesses in front of the grand jury for more than a month, essentially pausing their investigation into whether Mr. Trump inflated the value of his assets to obtain favorable loan terms from banks.

The precise reasons for Mr. Bragg’s pullback are unknown, and he has made few public statements about the status of the inquiry since taking office. In a statement responding to the resignations of the prosecutors, a spokeswoman for Mr. Bragg said that he was “grateful for their service” and that the investigation was ongoing.