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As Hillary Clinton courted African-Americans in Harlem on Wednesday, across Central Park, in the gilded ballroom at the Metropolitan Club, former President Bill Clinton sipped a pint of Guinness and addressed the Irish, another critical constituency as the Democratic contest descends on New York City.

Accepting a lifetime achievement award at the Irish America Hall of Fame luncheon for his role in bringing peace to Northern Ireland, Mr. Clinton, wearing a green tie, didn’t mention his wife’s presidential campaign. Instead, he talked about his own 1992 campaign, when, as governor of Arkansas, he tried to learn how to win a New York primary.

“What happened to me — and it sort of happened to me — began here in this city, late at night, almost exactly 24 years ago when I was trying to win the New York primary,” Mr. Clinton explained.

Back then, a group of powerful Irish Americans and sympathizers, including the Clinton adviser Harold M. Ickes and former Representative Bruce Morrison of Connecticut, had assembled to talk to Mr. Clinton about the fighting that plagued Northern Ireland and what the next president could do.

“They were grilling me about all matter of things, and I think they were surprised I was prepared,” he said.

Mr. Clinton won the bitterly contested New York primary in 1992, catapulting him to the nomination.

Years later, after he had helped to broker the Good Friday Agreement in 1998 that effectively ended the conflict in Northern Ireland, his daughter, Chelsea, wrote her senior thesis at Stanford about the history of Irish-American politics.

“She said, ‘You know, Dad, you didn’t care about this when you came to New York. You just wanted the Irish to vote for you,’” Mr. Clinton recalled.

“Well, not quite, but close enough,” he said. “‘But afterward, you really did care,’” Mr. Clinton said Chelsea told him.

Today, the Clintons enjoy some of their most loyal support from Irish-Americans, who remember their role in ending what are known as the Troubles. And that loyalty is likely to bolster Mrs. Clinton in the state’s April 19 primary.

As Mrs. Clinton spoke in Harlem alongside Senator Chuck Schumer of New York, the annual awards luncheon, hosted by Irish America Magazine, drew influential Irish politicians, business leaders and media personalities. Gen. Martin E. Dempsey, the former chairman of the Joint Chiefs of Staff, the astronaut Eileen M. Collins and the journalist and essayist Pete Hamill were also among the honorees.

As Ireland celebrates the 100th anniversary of the 1916 Easter Rising against British rule, Mr. Clinton delivered a poetic address, praising the Irish for their inclusive government and weaving lines of poetry from W.B. Yeats into his extemporaneous remarks. “Things fall apart, the center cannot hold,” Mr. Clinton said. “If the center does not hold, inclusive economics, inclusive societies, all fall to the politics of blame.”

Mr. Clinton urged Britain to remain in the European Union, afraid of the consequences for Northern Ireland should Britain vote to leave the union in a referendum in June.

“Northern Ireland would really get whacked if England left the European Union,” Mr. Clinton said. “I hope they don’t, because it’s easy to believe that the only solution to the modern world is to hunker down.”

“It’s a dangerous world out there,” Mr. Clinton continued, speaking on a pressing foreign policy issue that Mrs. Clinton has not yet addressed. “It’s easy to turn away, but it’s better to find a way to move forward because the enemies of freedom, the people who don’t believe in diversity, will always find a way to pierce the walls.”

“We can never let our hearts to turn to stone, and we can never let things fall apart so much that we cannot build a center where the future of our children counts more than the scars of our past,” Mr. Clinton concluded. “That is the ultimate lesson of every single thing that has happened from 100 years ago since that declaration was issued and all that has happened since 1995.”