WASHINGTON—President Donald Trump and John Kelly have settled on a truce, at least temporarily, to keep the chief of staff in place as the White House grapples with the turbulence of several senior departures and the prospect of further changes to come.

In a rare move, White House officials said there would be no major personnel changes Friday after a week when staff was distracted by reports that other senior officials, including national security adviser H.R. McMaster, may soon be heading for the exit.

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