President Donald Trump wasn’t happy. Sitting behind his desk in the Oval Office, he looked at the top aides assembled around him and said: “This has to go better.”

As they spoke last weekend, protests were mushrooming at airports around the country, prompted by travel restrictions imposed by executive order on seven Muslim-majority countries deemed to pose terrorist threats.

The temporary ban had morphed into a public-relations debacle. Lawmakers were blindsided. Government agencies puzzled over its meaning. Travelers were plucked from lines as they were boarding airplanes.

In the weekend meeting and another one on Monday, Jan. 30, Mr. Trump sought to avoid further confusion by clarifying the roles of senior staff members who had been jockeying for position since Election Day.