Despite his success, Mr. Buttigieg’s strategy presents some challenges. Accepting Silicon Valley money has become controversial at a time when big tech companies are under siege for lapses with privacy and misinformation. And his popularity with wealthy white liberals is great for fund-raising but so far has not helped him win much support from people of color, without whom no candidate can survive key early-primary contests in the South and West.

He still faces a big challenge in expanding his support among black voters, a critical constituency. He has recently been confronted by a local crisis, the fatal shooting of a black man by a white police officer in South Bend, which has tested his leadership.

Mr. Buttigieg had more than 230,000 new donors in the second quarter, bringing his total to more than 400,000, his campaign said. The average contribution over the course of his campaign has been $47.42, according to his team. His campaign said it now had more than $22.6 million in cash on hand. Of that, $832,000 is earmarked for the general election and cannot be used in the primary.

“This fund-raising report shows that Pete’s message is resonating with Americans, and it’s proof that we are building an organization that can compete,” Mike Schmuhl, his campaign manager, said in an early-morning email to supporters announcing the fund-raising total.

Mr. Buttigieg’s rivals have mostly favored one fund-raising approach or the other. Mr. Biden has concentrated his efforts on the broad network of Obama donors in major cities, but the 76-year-old former vice president hasn’t energized the small-dollar grass-roots world. Mr. Sanders and Ms. Warren have sworn off closed-door big-donor events as a political strategy aimed at creating a wider universe of small donors.

Senator Kamala Harris of California, who raised the second-highest amount of money during the year’s first reporting period, which ended March 31, is expected to have raised less in the second quarter than the $24.8 million that Mr. Buttigieg announced Monday.