Republican senators, including a member of the Senate’s leadership, accosted the director of the Secret Service in a suite at the Republican National Convention Wednesday night, demanding that she resign or provide a full explanation for the security lapses that led to the near-miss assassination attempt against former President Donald J. Trump.

Senators John Barrasso of Wyoming, the third-ranking Senate Republican, and Marsha Blackburn of Tennessee aggressively confronted the agency’s director, Kimberly A. Cheatle, at Fiserv Forum in Milwaukee. A staff member for one of the senators videotaped the confrontation and sent it to a reporter.

The video, which Ms. Blackburn also posted on X, shows Mr. Barrasso berating Ms. Cheatle over why Mr. Trump was allowed to go onstage for his Saturday evening rally in Butler, Pa., when authorities had already identified as suspicious a man who turned out to be the shooter, Thomas Matthew Crooks.

“You put him within less than an inch of his life,” Mr. Barrasso said to Ms. Cheatle, almost yelling. “So resignation or full explanation.”

Ms. Cheatle declined to answer their questions and instead walked out of the suite. Mr. Barrasso and Ms. Blackburn followed her down a corridor inside the arena and up a flight of stairs, continuing to yell questions at her and telling her she owed them answers.

Ms. Cheatle is in Milwaukee as the senior security official at the event. The Republican National Convention is a “national special security event,” the highest threat profile given by the federal government, because of its size and scope. Both Mr. Trump and his running mate, J.D. Vance, are under Secret Service protection.