An Oval Office meeting involving President Trump and his top advisers on Wednesday devolved into a heated exchange between his former campaign manager and the White House political director, people briefed on the discussion said.

The meeting centered on the midterm elections and came as Republicans face a daunting landscape next year, particularly after a bruising loss in the Alabama special election this month. It also came as the White House faces an expected string of departures from the West Wing, including that of a deputy chief of staff, Rick Dearborn, on Thursday. Mr. Dearborn, who was close to Jared Kushner and Ivanka Trump during the transition, had been overseeing a broad cross section of departments, including the political department, which was a source of contention during the meeting.

The meeting prompted the political director, Bill Stepien, to call an official at the main political group supporting Mr. Trump, America First Policies, to say its counsel should be involved at future gatherings.

It also underlined the turf battles and strategic disagreements that have long been characteristic of Mr. Trump’s circle, dating to his presidential campaign.