The pressure to disclose more about his work at McKinsey comes as the 37-year-old mayor also faces increased scrutiny about his lack of appeal to African-American voters, and amid increasing calls from Senator Elizabeth Warren of Massachusetts, who does not hold closed-door fund-raising events, to reveal details about his campaign’s fund-raising operation — including the names of his bundlers.

“This is about the conflicts that he is creating every single day right now,” Ms. Warren told reporters Saturday in New Hampshire.

For his part, Mr. Buttigieg has called on Ms. Warren to release more than the 11 years of personal tax returns she has already disclosed. Ms. Warren released a list of more than 50 legal clients in May.

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All of this comes as Mr. Buttigieg has established himself as the front-runner in Iowa, where Democrats hold the first-in-the-nation nominating caucuses Feb. 3. Democrats here are increasingly focused on selecting a candidate who will be the strongest in a general election against President Trump, who has refused to release any of his tax returns and did not divest himself from businesses that profit from his administration and campaign.

The pressure on Mr. Buttigieg to reveal more about his work at McKinsey is coming not only from his 2020 rivals like Ms. Warren, who in recent days has become far more aggressive in her attacks on him, but also from other Democratic politicians.

On Friday night in Waterloo, Iowa, Mayor Lori Lightfoot of Chicago, who had spoken favorably of Mr. Buttigieg just weeks earlier, told Mr. Buttigieg during an onstage interview that he should reveal for whom he did work at McKinsey.

“You said you can’t talk about your work at McKinsey because of a nondisclosure agreement, and I think you said today you’ve got to honor your commitment to McKinsey,” said Ms. Lightfoot, a corporate lawyer herself. “I’m asking you, should you break that N.D.A. so you have the moral authority and the high ground against somebody like Trump, who hides behind the lack of transparency to justify everything that he’s doing?”