In meetings, Mr. Trump appears to prefer Dr. Birx’s genial approach over Dr. Fauci’s blunt talk.

Mr. Trump and several White House officials view Dr. Fauci with some level of skepticism, believing he tends too much to his own public persona and has gone “rogue” on messaging. Dr. Birx, they think, is more willing to be patient with the president’s interruptions and theorizing about medicine.

Among Mr. Trump’s frustrations with Dr. Fauci has been his unwillingness to embrace the malaria drugs that Mr. Trump has celebrated, chloroquine and hydroxychloroquine. Dr. Fauci has been much more vocal about their risks, and dismissed potential evidence of their success in treating the coronavirus as anecdotal.