Washington girded for further change in President Donald Trump’s administration, as national security adviser H.R. McMaster’s position appeared increasingly precarious and a series of staff departures prompted a U.S. senator to publicly urge the president not to fire his attorney general.

Mr. Trump has decided to oust Lt. Gen. H.R. McMaster and has conveyed that decision to John Kelly, his chief of staff, according to administration officials. The timing of a departure was unclear, with one official saying it could happen...