In his tweet, Mr. Trump suggested more resignations may be coming: “I still have some people that I want to change (always seeking perfection).”

The New York Times and others reported on the cascading chaos of last week, with the announcement of the resignation of one of his longest-serving aides, Hope Hicks, and the threat of another staff resignation after Mr. Trump announced a new trade policy against the advice of one of his top economic advisers, Gary D. Cohn.

Mr. Cohn followed through on the threat late Tuesday afternoon, announcing that he would leave his post as director of the National Economic Council.

Mr. Trump’s son-in-law and senior adviser, Jared Kushner, had his security clearance downgraded, significantly limiting his access to some of the most serious national security issues the president faces. The White House also pushed back on rumors that Mr. Trump planned to fire his national security adviser, Lt. Gen. H.R. McMaster. Mr. Trump’s first national security adviser, Michael T. Flynn, resigned early last year and is cooperating with the special counsel in its ongoing investigation.

The president’s tweet about chaos was one of several on a range of topics, including immigration policy and the prospects of a denuclearized North Korea. Mr. Trump was also critical of the Oscars record-low ratings. He said, “Problem is, we don’t have Stars anymore — except your President (just kidding, of course)!”