And the financial pressure on those other candidates is now great: Former Mayor Pete Buttigieg of South Bend, Ind., left the campaign trail on Wednesday night and Thursday morning to raise money in New York, and former Vice President Joseph R. Biden Jr. and Senator Elizabeth Warren have been cutting back on their advertising after falling well short of victory in the Iowa caucuses, a development that could make it harder to raise money.

Senator Bernie Sanders, in turn, announced on Thursday that he had raised $25 million in January, a staggering sum. But Mr. Sanders is not dependent on the big-money donors whom Mr. Bloomberg has been pitching and whom Mr. Biden and Mr. Buttigieg are dependent on. As a result, Mr. Sanders, the most liberal candidate in the race, is now well positioned for a long primary race, especially if major donors heed Mr. Bloomberg’s overtures and embrace him over other moderates in the race.

Resembling fund-raisers in every aspect but one, Mr. Bloomberg’s events are organized under the auspices of a division of the campaign known as the Committee for Mike, a unit that closely resembles the structure of a traditional fund-raising operation — except that it does not actually solicit donations.

Unveiled last month, the Committee for Mike was described by the campaign as a network of influencers committed to Mr. Bloomberg’s candidacy. Its staff members have asked supporters to speak up for Mr. Bloomberg on social media and in personal conversations with their friends and colleagues, especially those who may reside in key primary states and general-election battlegrounds. Among the people managing the operation are former top fund-raisers for Senators Kamala Harris of California and Cory Booker of New Jersey.

Mr. Bloomberg has boasted throughout the campaign that he is immune to the influence of other people’s money, but with his fund-raising-style events he is signaling to people accustomed to giving big campaign contributions that he is at least open to their involvement.