[Which Democrats are leading the 2020 presidential race this week?]

“This is exciting proof of the momentum that we see on the ground across the country,” he wrote. “Powerful special interests and other campaigns are watching to see how ready we are to fight for big, structural change. And by hitting this first milestone, you’re helping to show them that change is coming sooner than they think.”

Mr. Sanders announced that he had crossed the million-donation threshold in April, and his campaign said Friday that it had reached two million donations on July 11. Through the end of June, he had raised about $36 million this cycle, more than Ms. Warren’s $25 million total. But his haul in the second quarter, $18 million, was slightly less than Ms. Warren’s in that period, which ran from April through June.

Attracting small donations from a large number of individuals has taken on even greater importance this cycle as the Democratic National Committee has made grass-roots fund-raising a qualification standard for the debates. To earn a spot on the debate stage in September, candidates must have received donations from at least 130,000 unique contributors, a bar that, as of Friday morning, only eight of the 24 candidates had met, according to a New York Times analysis. (Ms. Warren and Mr. Sanders are among those who have surpassed that number.)

[Cory Booker and Kamala Harris challenged Mr. Biden’s record on race ahead of the next debate.]

On Friday, Ms. Warren’s campaign did not specify how many individuals had made donations this cycle, only that one million donations were made over all. Donors can make multiple contributions over the course of the campaign.