The State Department is continuing an investigation of e-mail use among employees who worked for Hillary Clinton, the former secretary of state, asking scores of current and former officials to submit to questioning by the bureau overseeing diplomatic security, former officials said Sunday.

The investigation is examining whether employees used secure channels and the proper classification designations for what appeared to be routine e-mails, former officials said. The e-mails were on subjects that were not considered classified at the time, but that have been or are being retroactively marked as classified.

The e-mails were sent to Clinton while she was secretary of state from 2009 to 2013. They appear to have come to the attention of the diplomatic security bureau during earlier inquiries conducted by the State Department, Congress and the FBI into Clinton’s use of a private e-mail server.

The FBI director at the time, James Comey, said the bureau had found that Clinton did not engage in wrongdoing.

Sometime soon after President Donald Trump took office, the department’s diplomatic security bureau carried out the first stages of an investigation into e-mail use by employees under Clinton, former officials said.

The investigators appeared to want to finish the inquiry quickly and move on, former officials said. At some point, people who had heard of the investigation thought it had ended, officials said.

But in recent months the diplomatic security bureau has been interviewing current and former employees again about their e-mail use under Clinton, former officials said.

Former officials who described the current inquiry Sunday did so on the condition of anonymity, given the sensitivity of the matter. The State Department did not reply to a request for comment on the current investigation.

Former officials said scrutinizing employees over their handling of information that was not classified at the time, and only retroactively classified, was unusual.

In many cases, e-mails to Clinton were part of a long chain created by officials forwarding e-mails to one another.