The Environmental Protection Agency’s chief of staff said on Monday night that he, and not his boss, EPA Administrator Scott Pruitt, was responsible for substantial raises that were given to two top aides.

The chief of staff, Ryan Jackson, also said that the raises, worth tens of thousands of dollars, had been “reversed.“

Pruitt had come under fire for the raises, which were granted despite White House objections. He has also faced intense criticism—and calls for his resignation—for taking first-class...