WASHINGTON—The White House is bracing for more changes in the administration’s senior ranks following the recent departures of top officials including Secretary of State Rex Tillerson and Gary Cohn, director of the National Economic Council.

President Donald Trump prefaced a further shuffle as he departed for California Tuesday. “I’m really at a point where we’re getting very close to having the cabinet and other things that I want,” Mr. Trump said, hours after announcing via Twitter that he was replacing Mr. Tillerson with CIA Director Mike Pompeo.

Last week, on the day Mr. Cohn resigned, Mr. Trump said he was “always seeking perfection” in staffing the White House. But, he added: “There is no Chaos, only great Energy!”

In the past Mr. Trump has privately discussed ousting aides, only to reconsider, and at times he has publicly criticized cabinet members but taken no further action.

But White House officials say they are expecting more changes, which can come quickly once the president decides to show a colleague the exit. Some say Mr. Trump is keen to make the changes he wants to the lineup in advance of his meeting with North Korea’s Kim Jong Un, expected by May.