As he grappled on Thursday with his first major decision involving military action, a fed-up and frustrated President Donald Trump turned to his two top aides and told them he had had enough of their incessant knife-fights in the media.

“Work this out,” Trump said, according to two people briefed on the exchange. The admonition was aimed at Stephen Bannon, the tempestuous chief strategist, and Reince Priebus, the mild-mannered chief of staff, over a series of dustups with Jared Kushner, the president’s son-in-law and senior adviser, and the top economic adviser, Gary D. Cohn.

But they may not be able to.

The president is said to be aware that a meaningful reconciliation is unlikely between Bannon, who sees himself as the keeper of Trump’s campaign promises, and the competing ideologies of Kushner and Cohn, a longtime Wall Street executive and a Democrat. And he is considering a shake-up of his senior staff, according to four people with direct knowledge of the process.

Whether he acts on it remains to be seen. Trump has often pondered making changes for several weeks or even months before making them, if he does at all. He has a high tolerance for chaos, and a unique gift for creating it — and, despite his famous “You’re fired!” tagline from the show “The Apprentice,” an aversion to dismissing people.

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But this past week, one that some of his aides considered the best of his presidency, was marred by fits, starts and self-inflicted wounds — and the constant churn of news accounts of a White House at war with itself finally wore the president out. And notice of a possible shake-up was a warning shot to his team to make adjustments.

A spokeswoman for Trump, Sarah Huckabee Sanders, insisted that such accounts were untrue.

“Once again this is completely false story driven by people who want to distract from the success taking place in this administration,” she said in an emailed statement. “The President’s pick for the Supreme Court (a decision that has generational impact) was confirmed today, we hosted multiple foreign leaders this week and the President took bold and decisive military action against Syria last night. The only thing we are shaking up is the way Washington operates as we push the President’s aggressive agenda forward.”

But two people who have spoken with Trump said he recognised that the continuing state of drama was unsustainable.

No changes are imminent, they said. But the president is considering a range of options, including a shift in role for Bannon, who has become increasingly isolated in the White House as other power centres have grown, as well as additional senior staff.

Priebus has been a source of contention for a number of Trump’s former advisers, with the president pushing back on criticism with the response that the former chairman of the Republican National Committee is a “nice guy.”

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.

Bannon, whose portfolio is broad but vague as a chief strategist, has told people he believes 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 Bannon to a different role. His allies at an outside group supporting him run by his main benefactor, investor Rebekah Mercer, have also discussed him joining them to provide strategy.

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 Bannon made critical remarks about him to other aides and Trump associates while he was in Iraq recently. Bannon has told confidantes that he believes 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 Kushner is receiving from Breitbart News, the right-wing website that Bannon used to run.

But Bannon has his own core of supporters outside the White House. And he has argued that 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 Bannon believes so few Democrats would ever consider supporting Trump.

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

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.

There is a long history of presidents making staff changes, and one of Trump’s predecessors, Bill Clinton, made changes within the first six months of his administration.

Newt Gingrich, an informal adviser to Trump and a former House speaker, said, “I think first of all a very high amount of tension in the White House is normal.”

“I think they have particular tension right now because the health bill failed,” he added.

The stories about infighting “probably bother him some,” Gingrich said. “But do I think they’re damaging to his long-term prospects? I think they’re noise.”