The State Department is continuing an investigation of email 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 on Sunday.

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

The emails were sent to Mrs. Clinton while she was secretary of state from 2009 to 2013, in President Barack Obama’s administration. They appear to have come to the attention of the diplomatic security bureau during the earlier inquiries conducted by the State Department, Congress and the Federal Bureau of Investigation into Mrs. Clinton’s use of a private email server.

Although the F.B.I. director at the time, James B. Comey, said the bureau had found that Mrs. Clinton did not engage in wrongdoing, those earlier investigations threw a long shadow over the 2016 presidential campaign and are considered by Mrs. Clinton and many analysts to be a factor in President Trump’s victory.

The renewed focus on the emails was reported on Saturday by The Washington Post.

Sometime soon after Mr. Trump took office and appointed Rex W. Tillerson as his first secretary of state, the department’s diplomatic security bureau carried out the first stages of an investigation into email use by employees under Mrs. Clinton, the former officials said.

Most of the people being investigated were political appointees who were leaving or had already left the department.

The inquiry focused on the years when Mrs. Clinton was leading the State Department, even though many of the employees continued to work under her successor, John Kerry, the former officials said.

The investigators appeared to want to finish the inquiry quickly and move on, the former officials said. At some point during Mr. Tillerson’s tenure, people who had heard of the investigation thought it had ended because the diplomatic security bureau no longer appeared to be actively pursuing the question, the officials said.

Mike Pompeo took over as secretary of state in April 2018, and in recent months the diplomatic security bureau has been interviewing current and former employees again about their email use under Mrs. Clinton, the former officials said.

Before joining the Trump administration, Mr. Pompeo was a Republican member of the House, and served on the committee investigating the deadly raid on the American diplomatic compound in Benghazi, Libya. Mr. Pompeo was among those who aggressively questioned Mrs. Clinton.

The Justice Department inquiry into her use of a private email server had its roots in that congressional investigation, which brought to light Mrs. Clinton’s email practices.

The former officials who described the current inquiry on 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.

Looking to future prospects of the inquiry, the diplomatic security bureau could decide to make a formal note in a person’s file saying he or she had mishandled classified information, according to the former officials. That could lead to that person being unable to get proper security clearances in the future, or the applicant might have to wait a long time for those clearances to be approved.

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

Also, many of those emails summarize conversations with foreign officials who themselves have no security clearance in the United States government, yet are engaged in discussions about topics of interest to American counterparts. In many cases, the emails that went to Mrs. Clinton were part of a long email chain created by officials forwarding emails to one another.

Matthew Rosenberg contributed reporting.

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