Mr. Bannon, a hard-charging, fast-talking confidant of the president’s whose roving job in the White House has given him influence over policy and hiring decisions, now finds himself in the undesirable position of being caught between the president and his family. That is a position that others have not survived, most notably Corey Lewandowski, the first of the president’s three campaign managers.

Mr. Bannon, whose portfolio is broad but vague as a chief strategist, has told people he believes Mr. Kushner’s allies have undermined him, that he has no plans to quit and is digging in for a fight. One option being discussed is moving Mr. Bannon to a different role. His allies at an outside group supporting him run by his main benefactor, the investor Rebekah Mercer, have also discussed him joining them to provide strategy.

Mr. Kushner, 36, a government neophyte who has taken on a much larger portfolio as a top West Wing aide and foreign envoy, was said to be displeased after hearing that Mr. Bannon made critical remarks about him to other aides and Trump associates while he was in Iraq recently. Mr. Bannon has told confidants that he believes Mr. Kushner’s contact with Russians, and his expected testimony before Congress on the subject, will become a major distraction for the White House.

Kushner allies have also raised the issue with the president of the increasingly unflattering coverage that Mr. Kushner is receiving from Breitbart News, the right-wing website that Mr. Bannon used to run.

But Mr. Bannon has his own core of supporters outside the White House. And he has argued that Mr. Kushner’s efforts to pull his father-in-law more to the center on issues like immigration would poison him with the conservative base — a hopeless position to be in because Mr. Bannon believes so few Democrats would ever consider supporting Mr. Trump.

In the White House blame game, no one is safe. Mr. Bannon’s team is blamed for the contested and controversial travel bans. Mr. Priebus was damaged by the failure of health care legislation. Mr. Kushner has yet to show he can master his own portfolio, and his role is so large that miscues will be magnified.

Mr. Trump does not like any staff member gaining too much attention, including those who are related to him. He had three campaign shake-ups in the 2016 cycle, and he tends to make changes based on instinct. As he learns the job of a president, his allies say, he was destined to make such changes.