BOSTON — Senator Jeff Flake, the Republican who forced a new F.B.I. investigation into accusations against Judge Brett M. Kavanaugh, said on Monday that he was doing everything in his power to “make sure that any current, credible allegation that has been made is fully investigated.”

Mr. Flake’s comments came in response to a question from an interviewer at a Forbes Under 30 Summit at Boston’s City Hall Plaza. The interviewer had inquired about news reports regarding limits to the F.B.I. investigation that is set to run a week.

“We certainly want the F.B.I. to do a real investigation and we are working to make sure that that happens,” said Mr. Flake, of Arizona. “I’ve had discussions, many yesterday with my colleagues, and with the White House Counsel’s Office. My staff is following up as well.”

Mr. Flake, whose last-minute decision to seek an investigation upended proceedings in Washington last week, spoke on a temporary stage, under a light drizzle. The appearance here had been scheduled long before last week’s events. In a blue suit and tie, Mr. Flake appeared more relaxed than he had last week during the tense hearings. He smiled frequently during his remarks, especially when applauded by the crowd.