The clash came as two-thirds of American voters (66 percent) think the IRS targeted conservative groups as part of a high-level operation to punish political opponents.
Mr. Jordan, 49, then sought information on how many agents or investigators had been assigned to the case; what was the name of the lead investigator; whether agents had talked with any of the victims; and the status of those interviews.
"I may be able to do that, but I'd have to get back to you," the 68-year-old FBI chief said.
"Can you tell me who the lead investigator is?" Mr. Jordan asked again.
"Off the top of my head, no," Mr. Mueller responded.
At that point, Mr. Jordan suggested that the IRS case was "the most important issue in front of the country the last six weeks" and it came as a surprise that the FBI director didn't know the name of the lead investigator.