In an interview this week, Senator John Boozman of Arkansas said of Mr. Pruitt, “I think there are legitimate concerns about him.” He applauded Mr. Pruitt’s industry-friendly environmental policies, but said, “I think the president at some point is going to weigh in.” Mr. Boozman serves on the Senate environment panel as well as the powerful Appropriations Committee, which controls the E.P.A.’s spending.

On Thursday, John Cornyn of Texas, the No. 2 ranking member of the Senate, said that Mr. Pruitt was “just fine” on policy, “but obviously this controversy continues to swirl and it needs to be resolved, one way or the other.” Senator Lisa Murkowski of Alaska, chairwoman of the Senate Energy Committee, said she intended to summon Mr. Pruitt to her committee for questioning.

“The administration has a decision to make” on Mr. Pruitt’s future, she said.

Also on Thursday, the E.P.A.’s inspector general opened a new investigation into Mr. Pruitt’s use of the agency’s security team for personal travel.