WASHINGTON — Senior staff members at the Environmental Protection Agency frequently felt pressured by Scott Pruitt, the administrator, to help in personal matters and obtain special favors for his family, according to interviews with four current and former E.P.A. officials who served as top political aides to Mr. Pruitt.

The officials said that Mr. Pruitt, who “had a clear sense of entitlement,” in the words of one of them, indicated that he expected staff members’ assistance with matters outside the purview of government, including calling on an executive with connections in the energy industry to help secure tickets to a sold-out football game in January at the Rose Bowl.

The aides said the administrator — who is the subject of multiple investigations over ethics and other issues, but has been defended by President Trump as a champion of environmental deregulation — had also made it clear that he had no hesitation in leveraging his stature as a cabinet member to solicit favors himself.

At least three E.P.A. staff members were dispatched to help Mr. Pruitt’s daughter, McKenna, obtain a summer internship at the White House, the current and former staff members said.