Yet Mr. Trump is also frustrated with Mr. Kushner, whom he now views as a liability because of his legal entanglements, the investigations of the Kushner family’s real estate company and the publicity over having his security clearance downgraded, according to two people familiar with his views. In private conversations, the president vacillates between sounding regretful that Mr. Kushner is taking arrows and annoyed that he is another problem to deal with.

Privately, some aides have expressed frustration that Mr. Kushner and his wife, the president’s daughter Ivanka Trump, have remained at the White House, despite Mr. Trump at times saying they never should have come to the White House and should leave. Yet aides also noted that Mr. Trump has told the couple that they should keep serving in their roles, even as he has privately asked Mr. Kelly for his help in moving them out.