Republicans seized on Mr. Comey’s testimony last week as evidence that Ms. Abedin or Mr. Weiner should have been charged for how they handled classified information. Senator Ted Cruz of Texas brought up Mr. Comey’s comments on Monday in another hearing, asking James R. Clapper Jr., the former director of national intelligence, what he would have done if he learned that an employee “had forwarded hundreds or even thousands of emails to a nongovernment individual, their spouse, on a nongovernment computer.”

Mr. Clapper responded that if enough evidence were found, his office would have followed procedure and alerted the Justice Department that a crime was likely committed.

Mr. Comey said at last week’s hearing that the F.B.I. did not believe it had enough evidence to charge anyone with a crime in connection with Mrs. Clinton’s email server because it could not prove Mrs. Clinton or her aides intentionally broke the law.

“We could not prove that the people sending the information, either in that case or in the other case with the secretary, were acting with any kind of the mens rea — with any kind of criminal intent,” Mr. Comey said.

The New York Times noted in its coverage of Mr. Comey’s testimony on Wednesday that he had mischaracterized what the bureau had uncovered. A report late Monday in ProPublica saying that the F.B.I. was struggling to determine how to clarify Mr. Comey’s testimony set off a new round of criticism of his comments.

The investigation into Mrs. Clinton’s use of a private email server was a political liability throughout the 2016 presidential campaign. The case dragged on for months, contributed to Republican criticism that Mrs. Clinton was hiding something and created the spectacle of the Democratic front-runner being interviewed for hours at F.B.I. Headquarters last July.