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Mr. Liu's forceful critique of the federal agents looking into the legality of his donations, unprompted by a moderator or his rivals, captured his mounting frustration with an investigation that has cast a shadow over his fledgling campaign.

"Despite my record and despite my vision for the city, which I think is the right vision, there are still whispers about this cloud hanging over my head," Mr. Liu said in his closing statement at the forum, focused on poverty and income inequality.

His voice rising in anger, Mr. Liu listed his grievances: "Three years of investigating. They wiretapped my phones for 18 months. They reviewed a million documents and messages. They interrogated thousands of my supporters. And yet, what do they have to show for it? It's time to put up or shut up already. Because I have an election to win!"

The investigation dates back to 2009 and has resulted in the arrest of two associates — Mr. Liu's former 2013 campaign treasurer and a fund-raiser. Both are accused of conspiring to illegally funnel campaign contributions to Mr. Liu through "straw donors," or people whose contributions are reimbursed by others. Their trial is set to begin on April 15.

Mr. Liu has not been accused of wrongdoing, but documents and interviews have raised unflattering questions about his management style and integrity.

His decision to raise arguably his biggest political liability at a forum focused on issues like the minimum wage clearly caught his rivals by surprise.

"I was shocked," Tom Allon, a Republican candidate, said in an interview afterward. He compared Mr. Liu's sentiment to a dare.

"Catch me if you can," Mr. Allon said.

Mr. Liu's remarks, which drew loud applause from a crowd that seemed to be filled with his supporters, capped a lively and at times raucous forum at the First Corinthian Baptist Church in Harlem.

The City Council speaker, Christine C. Quinn, the perceived front-runner in the race, endured pointed and bipartisan barbs about her unwillingness to allow for a vote on paid sick leave and her fund-raising ties to developers.

Both Bill de Blasio, the city's public advocate and a Democratic mayoral candidate, and Mr. Allon demanded that Ms. Quinn reverse her position on legislation that would require many employers to provide paid sick leave to workers across the city. Ms. Quinn, who has kept the legislation from reaching the floor of the Council, has argued that such a requirement would hurt small businesses at a time when the economy is fragile.

"You have to give us a vote," Mr. de Blasio told Ms. Quinn.

Mr. Liu joined in on the jabbing. "There is no conclusive research," he said of Ms. Quinn's argument, "that paid sick leave is actually detrimental to the economy."

At one point, the moderator of the forum, Brian Lehrer, asked whether there was anyone on stage besides Ms. Quinn who opposed paid sick leave now. No one raised their hand.

Ms. Quinn said she was carefully studying when the city might be ready for such a measure, which she supports in theory. But when Mr. Lehrer asked her which specific economic metric she would use to determine the right time, she replied, "We are evaluating that; I can't tell you that there is one."

All but one of the candidates said that New York should follow President Obama's plan to raise the minimum wage to $9 an hour. Mr. Liu, to ferocious applause, called for the state to raise the minimum wage to $11.50 an hour over the next few years, over the current $7.25.

Two major Republican candidates, Joseph J. Lhota and John Catsimatidis, did not attend, a fact that Mr. Lehrer noted.

The night was filled with unexpected glimpses into the candidates' personal lives. William C. Thompson Jr., the Democratic mayoral nominee in 2009 and a candidate again this year, recalled warning his 15-year-old stepson how to react if he were stopped and frisked by the police.

"If I am not doing anything wrong," Mr. Thompson recalled the boy asking, "why would I be stopped?" Mr. Thompson said that the police tactic "has been misused and abused."