WASHINGTON — The State Department on Friday said for the first time that “top secret” material had been sent through Hillary Clinton’s private computer server, and that it would not make public 22 of her emails because they contained highly classified information.

The department announced that 18 emails exchanged between Mrs. Clinton and President Obama would also be withheld, citing the longstanding practice of preserving presidential communications for future release. The department’s spokesman, John Kirby, said that exchanges did not involve classified information.

The disclosure of the top secret emails, three days before Iowans vote in the first-in-the-nation caucuses, is certain to fuel the political debate over the unclassified computer server that Mrs. Clinton, the front-runner for the Democratic presidential nomination, kept in her home. The State Department released another set of her emails on Friday night in response to a Freedom of Information Act request.

The top secret emails lent credence to criticism by Mrs. Clinton’s rivals in the presidential race of her handling of classified information while she was secretary of state from 2009 to 2013. It is against the law for officials to discuss classified information on unclassified networks used for routine business or on private servers, and the F.B.I. is looking into whether such information was mishandled.