WASHINGTON—White House Chief of Staff John Kelly told President Donald Trump last week that he is convinced Environmental Protection Agency chief Scott Pruitt needs to step down after a series of negative reports about his spending habits and management style, a White House official said Friday.

Though Mr. Kelly and other White House aides have concluded Mr. Pruitt should leave, the president is not ready to fire him, the official said. Mr. Trump welcomes the deregulatory measures taken by Mr. Pruitt and also values him as a strong advocate for the president’s agenda, this person said.

The president, in a tweet Friday, said Mr. Pruitt is doing “a great job,” adding that he is “TOTALLY under siege.”

That comment follows remarks aboard Air Force One on Thursday in which he described Pruitt as doing “a fantastic job.” He also said Mr. Pruitt is a “fantastic person,” adding that he still has confidence in the EPA administrator.

However, the president said he would look into the various controversies surrounding Mr. Pruitt. “I have to look at them,” Mr. Trump said, during a flight home from a public appearance in West Virginia. “I’ll make that determination.”