By David Benoit 

Larry Fink, the boss of the world's biggest money manager BlackRock Inc., has spent the past few years labeling Carl Icahn and his activist ilk a danger for companies. Wednesday, Mr. Icahn flipped the script.

"BlackRock is an extremely dangerous company," Mr. Icahn announced at CNBC's Delivering Alpha conference in New York.

The two famed investors sparred on stage at the conference, with laughs from the audience, though Mr. Fink showed obvious irritation as the criticism continued. Mr. Icahn steered the bulk of the conversation away from activism--the billing of the event--to his growing fears about a bubble in high-yield bonds and what he called the dangers of exchange-traded funds run by firms like Mr. Fink's.

Mr. Icahn blamed the growing prices for such relatively risky debt partly on Mr. Fink's sprawling $4 trillion asset manager and its exchange-traded funds, which Mr. Icahn said were causing a liquidity problem because they have snapped up so many assets.

Mr. Icahn is concerned because ETFs now own so many assets and Wall Street firms are retreating from trading, which he says raises questions about who will buy if investors sell ETFs during the next market downturn.

Exchange-traded funds are securities that trade on an exchange and typically track an index or other basket of assets.

Mr. Icahn argued junk-bond ETFs will be much harder to trade in the next downturn than most investors expect, leading to big losses, especially for individuals who have flocked to these products in recent years.

Mr. Fink had some different ideas.

"ETFs create more transparency in the market, especially high-yield," Mr. Fink said, chiding that Mr. Icahn had gotten the picture wrong. "Carl, once again, you are a good investor, but you are wrong again, you are just dead wrong."

Mr. Fink said the ETFs are a way to buy exposure and aren't crimping liquidity.

The scene drew laughs from the audience, and Mr. Icahn several times looked to clarify his views weren't against Mr. Fink personally, or BlackRock.

"It's his job to make money," he said.

At one point, Mr. Icahn described a cartoon he was imagining to get across his point. It would involve a party bus of sorts full of bond investors drinking and having a good time, and unaware they are heading toward a cliff.

"You know who is pushing it? Larry Fink and Janet Yellen," Mr. Icahn said with a laugh, referring to the chairwoman of the Federal Reserve. "You know what's going to destroy it? They are going to hit a black rock."

Mr. Icahn has recently looked to make a public warning about what he sees as a bubble in high-yield bonds and Wednesday resisted letting the conversation wander far from his concerns to the scheduled topic of activism.

Mr. Fink declined to say whether there was a bubble or not. He did offer to take Mr. Icahn to lunch, and foot the bill, for a lesson on ETFs, a plan Mr. Icahn was willing to take him up on.

About activism, the two did find some time to disagree as well, with Mr. Fink saying some activists are pushing poor short-term decisions and Mr. Icahn saying BlackRock is enabling poor corporate executives.

Mr. Fink said his firm supports activists more often than many think, which some data supports, though Mr. Icahn claimed he had never won a BlackRock vote.

Gregory Zuckerman contributed to this article

Write to David Benoit at david.benoit@wsj.com

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