The decision, announced in January 2009, came after the health insurance provider reported a loss of about $140 million primarily related to health care plans purchased by individuals. The company also announced that it was freezing pay for nonunion workers and cutting discretionary spending by 25 percent. In an interview published Tuesday by The Atlantic, Mr. Buttigieg said he was taken off the Blue Cross project in 2007, well before the layoffs were announced.

But when he was running for mayor of South Bend in 2011, Mr. Buttigieg seemed to refer to his tenure at Blue Cross as evidence that he had the skills necessary “to reimagine our budget from the bottom up.”

“One of the things I did for a living was just that,” Mr. Buttigieg said during a candidate forum. “So I remember one client organization that was a large insurance firm that had grown in such a way that there was a great deal of duplication and some people didn’t even know what the people working for them were doing.”

On MSNBC Tuesday, Mr. Buttigieg said his work with Blue Cross had “nothing to do with claims or what they do with patients.” Asked by host Rachel Maddow if his work led to layoffs, Mr. Buttigieg replied: “I doubt it. I don’t know what happened after the time that I left, in 2007, when they decided to shrink in 2009.”

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The list of Buttigieg clients also included the United States Postal Service, which had called in McKinsey in an effort to stem growing losses in its revenues as use of the mail declined.

A report prepared by McKinsey in 2010 suggested that the Postal Service cut costs by replacing career employees with other workers and reduce benefits to bring them more in line with the private sector.

Mr. Buttigieg’s Afghanistan work was done as the United States was spending millions in an effort to boost the country’s economy. Much of that work focused on looking for ways to extract and market Afghanistan’s rich natural resources, including huge veins of iron, copper, cobalt, gold and industrial metals like lithium.