[What you need to know to start the day: Get New York Today in your inbox.]
Both were enduring characters in New York, their names in headlines, their faces on television. Both began their lives outside Manhattan — one was born in Brownsville, Brooklyn, the other in Jamaica, Queens — and both worked their way toward its irresistibly sizzling spotlight. Both found fame on television, Donald J. Trump as a reality-show host, the Rev. Al Sharpton as a cable news commentator.
They occasionally crossed paths, drawing energy from each other even as foes, as Mr. Trump made claims that Mr. Sharpton challenged — about five black teenagers who were charged with raping a jogger in Central Park in the 1980s, and about whether Barack Obama was born in the United States.
But sometimes they were friends in the way that public figures in New York can be. Mr. Trump cut the ribbon at Mr. Sharpton’s National Action Network annual convention in 2002. And in 2006, Mr. Trump returned to the convention, standing next to Mr. Sharpton, the Rev. Jesse Jackson and the singer James Brown.
“Different tune now,” Mr. Sharpton observed on Monday.
The two have once again found themselves convenient foils, after President Trump denounced Representative Elijah E. Cummings, calling the African-American congressman, a Democrat who represents much of Baltimore, “racist,” and his district a “disgusting, rat and rodent infested mess.”
On Monday, the president seized on a Twitter post from Mr. Sharpton, who said he was on his way to Baltimore. Mr. Trump assailed Mr. Sharpton as “a con man” who “Hates Whites & Cops!”
The president and Mr. Sharpton agreed on at least one thing — that they had known each other for 25 years. Mr. Trump said so on Twitter, Mr. Sharpton at a news conference in Baltimore.
“Went to fights with him & Don King, always got along well,” Mr. Trump wrote. “He ‘loved Trump!’ He would ask me for favors often. Al is a con man, a troublemaker, always looking for a score. Just doing his thing. Must have intimidated Comcast/NBC. Hates Whites & Cops!”
Mr. Sharpton shrugged off the idea that he was a troublemaker. “Yes, I make trouble for bigots,” he said. “I made trouble for him in Central Park. I made trouble for him with birtherism.”
“As far as me being a con man, if he really thought I was a con man, he’d be nominating me for his cabinet,” Mr. Sharpton said, to laughter at the news conference, before noting that Mr. Trump had called him “right after he was elected.”
In earlier interviews, Mr. Sharpton has also mentioned anecdotes involving him, Mr. Trump and Mr. King, the boxing promoter.
“Don King had me fly with him and Trump to Atlantic in Trump’s helicopter, and it was one of the most memorable things in my life to sit on a helicopter, big, black Trump helicopter with Don King and Donald Trump, both of them talking nonstop, not listening to each other,” Mr. Sharpton said in a 2016 interview with Politico about a trip to Atlantic City.
“Donald Trump knows deep down in his heart that I believe in what I’m doing, and I know that he believes in what he’s doing,” Mr. Sharpton said then. “He believes in Donald Trump.”
The president, in a follow-up Twitter post on Monday, suggested that in a more recent encounter, Mr. Sharpton visited Mr. Trump at Trump Tower “during the presidential campaign to apologize for the way he was talking about me.”
Mr. Sharpton said the episode never happened.
“Him saying that I met with him during the campaign in ’16 is a lie,” he said.
Mr. Sharpton did not seem in an apologetic mood on Monday, accusing the president of “playing a race-divisive card” and saying that Mr. Trump “has a particular venom for blacks and people of color.”
“He attacks Nancy Pelosi, he attacks Chuck Schumer, he attacks other whites, but he never said that their districts or their states are places that no human being wants to live,” Mr. Sharpton said.