By that point, Mr. Trump’s relationship with Mr. Flynn had grown more awkward. One person close to the president, who asked to remain anonymous to describe private discussions, said Mr. Trump had been “uncomfortable” with Mr. Flynn for weeks. Jared Kushner, the president’s son-in-law and senior adviser, had expressed concern about Mr. Flynn’s appointment even before the inauguration, according to another person briefed on the discussions.

Mr. Trump’s views were coming around to the same point. “What he knew was that Flynn was too much about Flynn, versus Mattis,” the person close to the president said. Defense Secretary Jim Mattis was seen as deferential to the chain of command. “He loves Mattis because Mattis is respectful and self-confident.”

Another key figure with growing concerns about Mr. Flynn was Stephen K. Bannon, the president’s chief strategist whom Mr. Flynn perceived as a rival for control over national security. Mr. Trump began asking Mr. Mattis about two weeks ago for suggestions of possible replacements for Mr. Flynn. The defense secretary recommended retired Vice Adm. Robert S. Harward. Mr. Bannon reached out to Mr. Harward last week, two senior officials said.