For his federal campaign, Mr. de Blasio said he would go further than the required rules and refuse donations from people who are listed in the city’s “doing business” database. But that did not stop him from calling those people and asking them for help.

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In the calls he made in September, Mr. de Blasio did not talk as if the end was near in his telephone pitch. He still held out hope of qualifying for the October debate — which came and went without him last Tuesday.

David Weinraub, an Albany-based lobbyist on the list, said he got a call from the mayor last month.

“I hadn’t talked to him in a long time,” Mr. Weinraub said. “I said, ‘What do you need, a zillion smaller donors?’ And he said no, I got that,’” he recalled the mayor saying confidently. (Mr. de Blasio was relying on an endorsement by the city’s hotel union, which provided him with thousands of low-dollar contributions to his campaign.)

“The goal then was that he was going to try to get into the October debate,” Mr. Weinraub recalled, “and he said he actually needed some big donors.”

Mr. Weinraub asked his son, Frederick, an employee of the lobbying firm, if he would be willing to give his own money. He did so.

A spokesman for the mayor’s presidential campaign, Jon Paul Lupo, said in a statement that “the mayor has not accepted money from any person on New York City’s ‘doing business list,’” adding that “many factors” went into Mr. de Blasio’s decision to end the campaign.

Another donor, who requested anonymity to discuss the conversation with the mayor, said Mr. de Blasio called one evening last month after a long day.