In a statement, Mr. Buttigieg, 38, who recently finished his second term as mayor of South Bend, Ind., nodded to those challenges and struck a progressive tone in emphasizing the importance of supporting his staff.

“We’re proud of the staffers who stood up and made their voices heard to help our campaign improve and be more inclusive,” Mr. Buttigieg said. “We realize that we can always do better and these honest discussions are how we make progress, and we will continue to provide our staff the safe space to have them.” His campaign provided the statement in response to questions about the operation.

Vernon Gair, the accounting director for the campaign, who was made available by officials there, said that because of Mr. Buttigieg’s struggle to attract black voters, the campaign had to meet a higher bar internally in addressing the concerns of minority employees. “We can’t just be good enough on these issues — our candidates, and our teams,” Mr. Gair, who is black, said in an interview.

He said he was a member of what the campaign called “bridge” groups aimed at providing support to staff members who were members of certain affinity groups, including black and L.G.B.T.Q. employees. Mr. Gair said his group had conveyed some of its frustrations to the campaign manager, Mike Schmuhl, who took the time to listen. Mr. Gair declined to be specific about the frustrations.

After this article was published on Tuesday, the Buttigieg campaign posted a lengthy explanation of its diversity efforts online. “Pete for America is committed to creating trusted environments for issues to be raised and addressed within, across and outside the campaign,” the campaign wrote. “We are proud of our efforts and we are especially proud of our staff.

While concerns about diversity are not uncommon for people working in other political campaigns, the flurry of activity inside Buttigieg headquarters related to workplace culture is unusual so close to the start of voting, said Donna Brazile, a veteran of Democratic presidential campaigns since 1984.

“I’ve never heard of anything like this,” Ms. Brazile said. “Not in ’08 and never in 2016.”

Robby Mook, who managed Hillary Clinton’s 2016 campaign, said campaigns were becoming more open to hearing from junior staff members whose concerns in the past may have been largely ignored by top officials.