The Benghazi committee, in the course of its investigation, discovered that Mrs. Clinton had used her personal email account for State Department business.

Mrs. Clinton has said for months that she kept no classified information on the private server she had set up in her house so that she would not have to carry both a personal phone and a work phone. Her campaign said on Friday that any government secrets found on the server had been classified after the fact.

Campaigning in Iowa on Saturday, she was asked about the email issue. “I think there’s so much confusion around this that I understand why reporters and the public are asking questions, but the facts are pretty clear,” she told reporters, according to The Associated Press. “I did not send nor receive anything that was classified at the time.”

But the two inspectors general said on Friday that the information they found was classified when it was sent and remains so. Information is considered classified if its disclosure would be likely to harm national security. The investigators said the information was not marked as classified but should have been stored only on government computer networks with special safeguards.

“This classified information never should have been transmitted via an unclassified personal system,” Steve A. Linick, the State Department inspector general, said in a statement signed by him and I. Charles McCullough III, the inspector general for the intelligence agencies.

Saturday’s testy back-and-forth seemed to boil down to a spat about who should have announced Mrs. Clinton’s agreement to testify. It also pointed up how contentious the subject of her email account remains — and that it is only likely to grow as 2016 draws near.

The Oct. 22 date would give the committee months to receive from the State Department, and then digest, troves of email traffic involving Mrs. Clinton’s aides. And her testimony would take place when more people were focused on her campaign.