In an interview with The Wall Street Journal on Wednesday, Mr. Trump made clear Mr. Bannon’s subordinate role, calling him “a guy who works for me.”

Amid the clashing egos, news media leaks and insinuations of disloyalty, the president was once again faced with having to defuse a personnel crisis that was, in part, a result of assembling a band of Washington outsiders to run his administration. And this time the crisis erupted, perhaps predictably, around the senior aide who most embodies that renegade, anti-establishment ethos: Mr. Bannon, the self-proclaimed deconstructor of the “administrative state” and field general in the war against the “opposition party” news media.

Mr. Bannon’s reversal of fortunes is also a reflection of a White House with an unconventional management structure, opaque lines of responsibility and rafts of aides left to carry out complex and contested campaign promises: tighten immigration, roll back regulations, repeal the Affordable Care Act and take a more protectionist approach to trade.

Mr. Bannon, who has those campaign promises scrawled on white boards in his office, has described himself as being responsible for their implementation. But the execution has been botched. Courts have blocked the president’s immigration ban. The repeal effort failed after the White House and congressional leaders could not win enough support in their own party. And that is leaving some conservatives, who have never fully trusted the president’s convictions, afraid that Mr. Bannon’s possible removal could be a precursor to shelving the most complicated and contentious priorities.

One person with firsthand knowledge of internal White House dynamics, who asked not to be identified given how tense the situation had become, insisted that no immediate changes were likely. Mr. Trump is notoriously fickle in his decision-making process, and he dislikes confrontation. But by openly criticizing Mr. Bannon, he has created an environment that makes it hard for the swaggering and self-assured chief strategist to remain in place without appearing undermined.